MathModDB: An Ontology for Mathematical Models
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MathModDB: An Ontology for Mathematical Models

This version:
https://mardi4nfdi.de/mathmoddb/0.1
Revision:
0.8.0
Issued on:
2025-01-20
Authors:
Aurela Shehu (https://orcid.org/0000-0002-1994-0612), Weierstrass Institute Berlin for Applied Analysis and Stochastics (https://ror.org/00h1x4t21, https://isni.org/isni/000000010066936X)
Björn Schembera (https://orcid.org/0000-0003-2860-6621), Universität Stuttgart (https://ror.org/04vnq7t77, https://isni.org/isni/0000000419369713)
Burkhard Schmidt (https://orcid.org/0000-0002-9658-499X), Weierstrass Institute Berlin for Applied Analysis and Stochastics (https://ror.org/00h1x4t21, https://isni.org/isni/000000010066936X)
Christine Biedinger (https://orcid.org/0009-0002-5082-8386), Fraunhofer Institute for Industrial Mathematics ITWM (https://ror.org/019hjw009)
Jochen Fiedler (https://orcid.org/0000-0002-9176-780X), Fraunhofer Institute for Industrial Mathematics ITWM (https://ror.org/019hjw009)
Marco Reidelbach (https://orcid.org/0000-0002-1919-1834), Zuse Institute Berlin (https://ror.org/02eva5865, https://isni.org/isni/000000011010926X)
Thomas Koprucki (https://orcid.org/0000-0001-6235-9412), Weierstrass Institute Berlin for Applied Analysis and Stochastics (https://ror.org/00h1x4t21, https://isni.org/isni/000000010066936X)
Publisher:
MaRDI (https://www.mardi4nfdi.de)
See also:
https://doi.org/10.1007/978-3-031-65990-4_14
https://doi.org/10.48550/arXiv.2408.10003
https://doi.org/10.52825/cordi.v1i.255
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License:
https://creativecommons.org/licenses/by/4.0/
Visualization:
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Cite as:
Shehu, A., Schembera, B., Schmidt, B., Biedinger, C., Fiedler, J., Reidelbrach, M., Koprucki, T. (2025): MathModDB. An Ontology for Mathematical Models
Provenance of this page
Ontology Specification Draft

Abstract

MathModDB is a database of mathematical models developed by the Mathematical Research Data Initiative (MaRDI). MathModDB defines a data model with classes (Mathematical Model, Mathematical Formulation, Research Field, Research Problem, Quantity [Kind], [Computational] Task, Publication), object properties/relations, data properties and annotation properties as an ontology. This ontology is populated with individuals/data from various fields of applied mathematics, making it a knowledge graph.

Introduction back to ToC

Test 1 2 3 4

MathModDB Ontology: Overview back to ToC

This ontology has the following classes and properties.

Classes

Object Properties

Data Properties

Annotation Properties

Named Individuals

MathModDB Ontology: Description back to ToC

This is the MathModDB Ontology for documenting mathematical models.

Cross-reference for MathModDB Ontology classes, object properties and data properties back to ToC

This section provides details for each class and property defined by MathModDB Ontology.

Classes

Computational Taskc back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathmoddb#ComputationalTask

A specific computational task associated with a mathematical model. Typically, various tasks differ from each other by the choice of given quantities (input), unknown quantities (output), parameters or constants as well as boundary conditions, initial conditions and/or final conditions.
has super-classes
Task c
is in domain of
applies model op, approximated by task op, approximates task op, contained in task op, contains assumption op, contains boundary condition op, contains constant op, contains constraint condition op, contains coupling condition op, contains final condition op, contains formulation op, contains initial condition op, contains input op, contains objective op, contains output op, contains parameter op, contains task op, discretized by task op, discretizes task op, documented in op, generalized by task op, generalizes task op, invented in op, is linear dp, linearized by task op, linearizes task op, similar to task op, studied in op, surveyed in op, used in op
is in range of
applied by task op, approximated by task op, approximates task op, contained as assumption in op, contained as boundary condition in op, contained as constant in op, contained as constraint condition in op, contained as coupling condition in op, contained as final condition in op, contained as formulation in op, contained as initial condition in op, contained as input in op, contained as objective in op, contained as output in op, contained as parameter in op, contained in task op, contains task op, discretized by task op, discretizes task op, documents op, generalized by task op, generalizes task op, invents op, linearized by task op, linearizes task op, similar to task op, studies op, surveys op, uses op
has members
Balanced Truncation ni, Balanced Truncation (Bi-linear) ni, Balanced Truncation (Linear) ni, Calculation of Deformation and Concentration ni, Classical Time Evolution ni, Control System Time Evolution ni, Control System Time Evolution (Bi-linear) ni, Control System Time Evolution (Linear) ni, Denoising for Improved Parametric MRI of the Kidney ni, Extract Logical Rules ni, Far Field Radiation ni, Free Fall Determine Gravitation ni, Free Fall Determine Time ni, Free Fall Determine Velocity ni, H2 Optimal Approximation ni, H2 Optimal Approximation (Bi-linear) ni, H2 Optimal Approximation (Linear) ni, Linear Parameter Estimation (Uni Uni Reaction without Product - Eadie Hofstee Model - Irreversibility Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product - Eadie Hofstee Model - Rapid Equilibrium Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product - Eadie Hofstee Model - Steady State Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product - Hanes Woolf Model - Irreversibility Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product - Hanes Woolf Model - Rapid Equilibrium Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product - Hanes Woolf Model - Steady State Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product - Lineweaver Burk Model - Irreversibility Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product - Lineweaver Burk Model - Rapid Equilibrium Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product - Lineweaver Burk Model - Steady State Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Dixon Model - Steady State Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Eadie Hofstee Model - Steady State Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Hanes Woolf Model - Steady State Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Lineweaver Burk Model - Steady State Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Dixon Model - Steady State Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Eadie Hofstee Model - Steady State Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Hanes Woolf Model - Steady State Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Lineweaver Burk Model - Steady State Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Dixon Model - Steady State Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Eadie Hofstee Model - Steady State Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Hanes Woolf Model - Steady State Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Lineweaver Burk Model - Steady State Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Dixon Model - Steady State Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Eadie Hofstee Model - Steady State Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Hanes Woolf Model - Steady State Assumption) ni, Linear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Lineweaver Burk Model - Steady State Assumption) ni, Linear Parameter Estimation of Enzyme Kinetics ni, Mathematical Analysis of DHW Equation ni, Maximizing Poisson log-Likelihood ni, Maximum Likelihood Estimation ni, Model Order Reduction ni, Near Field Radiation ni, Nonlinear Parameter Estimation (Uni Uni Reaction with Product - Michaelis Menten Model - Steady State Assumption) ni, Nonlinear Parameter Estimation (Uni Uni Reaction without Product - Michaelis Menten Model - Irreversibility Assumption) ni, Nonlinear Parameter Estimation (Uni Uni Reaction without Product - Michaelis Menten Model - Rapid Equilibrium Assumption) ni, Nonlinear Parameter Estimation (Uni Uni Reaction without Product - Michaelis Menten Model - Steady State Assumption) ni, Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Michaelis Menten Model - Steady State Assumption) ni, Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Competitive Partial Inhibition - Michaelis Menten Model - Steady State Assumption) ni, Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Michaelis Menten Model - Steady State Assumption) ni, Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Mixed Partial Inhibition - Michaelis Menten Model - Steady State Assumption) ni, Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Michaelis Menten Model - Steady State Assumption) ni, Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Non-Competitive Partial Inhibition - Michaelis Menten Model - Steady State Assumption) ni, Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Michaelis Menten Model - Steady State Assumption) ni, Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Partial Inhibition - Michaelis Menten Model - Steady State Assumption) ni, Nonlinear Parameter Estimation of Enzyme Kinetics ni, Optimal Control ni, Parameter Estimation of Enzyme Kinetics ni, Quantum Conditional Quasi-Solvability ni, Quantum Stationary States ni, Quantum Time Evolution ni, Romanization Parameter Estimation ni, Romanization Time Evolution ni, Semiconductor Charge Neutrality ni, Semiconductor Current Voltage ni, Semiconductor Thermal Equilibrium ni, Sensitivity Analysis of Complex Kinetic Systems ni, Simulation of Complex Kinetic Systems ni, Simulation of TEM Images ni, Sorting Objects ni, Symmetry Analysis In TEM Images ni
is disjoint with
Mathematical Formulation c, Mathematical Model c, Publication c, Quantity c, Quantity Kind c, Research Field c, Research Problem c

Mathematical Formulationc back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathmoddb#MathematicalFormulationDefinition

Typically, a mathematical formulation is based on equations (general construct indicating equality of quantities) or on inequalities (non-equal relations between quantities), or a logic quantifier
is in domain of
approximated by formulation op, approximates formulation op, contained as assumption in op, contained as boundary condition in op, contained as constraint condition in op, contained as coupling condition in op, contained as final condition in op, contained as formulation in op, contained as initial condition in op, contains assumption op, contains boundary condition op, contains constant op, contains constraint condition op, contains coupling condition op, contains final condition op, contains formulation op, contains initial condition op, contains quantity op, defines op, defining formulation dp, discretized by formulation op, discretizes formulation op, documented in op, formulation property dp, generalized by formulation op, generalizes formulation op, in defining formulation dp, invented in op, is convex dp, is deterministic dp, is dimensionless dp, is dynamic dp, is linear dp, is space-continuous dp, is time-continuous dp, linearized by formulation op, linearizes formulation op, nondimensionalized by formulation op, nondimensionalizes formulation op, similar to formulation op, studied in op, surveyed in op, used in op
is in range of
approximated by formulation op, approximates formulation op, contained as assumption in op, contained as boundary condition in op, contained as constant in op, contained as constraint condition in op, contained as coupling condition in op, contained as final condition in op, contained as formulation in op, contained as initial condition in op, contained in formulation op, contains assumption op, contains boundary condition op, contains constraint condition op, contains coupling condition op, contains final condition op, contains formulation op, contains initial condition op, defined by op, discretized by formulation op, discretizes formulation op, documents op, generalized by formulation op, generalizes formulation op, invents op, linearized by formulation op, linearizes formulation op, nondimensionalized by formulation op, nondimensionalizes formulation op, similar to formulation op, studies op, surveys op, uses op
has members
Active Contractile Force (Definition) ni, Allee Effect ni, Ampere Law ni, Anharmonicity Constant (Definition) ni, Attraction Force At Opinion Formulation ni, Average Opinion Of Followers Of Infuencers Formulation ni, Average Opinion Of Followers Of Infuencers In The Partial Mean Field Model Formulation ni, Average Opinion Of Followers Of Media Formulation ni, Average Opinion Of Followers Of Media In The Partial Mean Field Model Formulation ni, Balancing Transformation ni, Beavers–Joseph-Saffman Condition ni, Between Population Contact Rate Equation ni, Bi Bi Reaction Ordered Mechanism ODE System ni, Bi Bi Reaction Ordered Mechanism with single central Complex ODE System ni, Bi Bi Reaction Ping Pong Mechanism ODE System ni, Bi Bi Reaction Theorell-Chance Mechanism ODE System ni, Boltzmann Approximation For Electrons ni, Boltzmann Approximation For Holes ni, Boundary Conditions of Electrophysiological Muscle ODE System ni, Change In Opinions Of Individuals ni, Change In Opinions Of Influencers ni, Change In Opinions Of Influencers In The Partial Mean Field Model ni, Change In Opinions Of Media ni, Change In Opinions Of Media In The Partial Mean Field Model ni, Classical Approximation ni, Classical Brownian Equation ni, Classical Fokker Planck Equation ni, Classical Hamilton Equations ni, Classical Hamilton Equations (Leap Frog) ni, Classical Langevin Equation ni, Classical Liouville Equation ni, Classical Momentum (Definition) ni, Classical Newton Equation ni, Classical Newton Equation (Stoermer Verlet) ni, Closed System Approximation ni, Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition, Definition) ni, Condition For Positive Solutions In The Multi-Population SI Model ni, Condition For Positive Solutions In The Multi-Population SIR Model ni, Condition For Positive Solutions In The Multi-Population SIS Model ni, Condition For Positive Solutions In The SIR Model ni, Condition For Positive Solutions In The SIR Model with Births and Deaths ni, Condition For Positive Solutions In The SIS Model ni, Condition For Positive Solutions In The SIS Model with Births and Deaths ni, Condition To Keep Susceptibles Positive ni, Conservation Law ni, Conservation of City Numbers ni, Constant Population Size ni, Contact Network (Definition) ni, Contact Network (Time-dependent, Definition) ni, Contact Network Constraint ni, Continuity Equation ni, Continuity Equation For Electrons ni, Continuity Equation For Electrons (Finite Volume) ni, Continuity Equation For Holes ni, Continuity Equation For Holes (Finite Volume) ni, Continuity of the Normal Mass Flux ni, Continuity of the Normal Stresses ni, Continuous Rate of Change of Infectious in the SI Model ni, Continuous Rate of Change of Infectious in the SIR Model ni, Continuous Rate of Change of Removed in the SIR Model ni, Continuous Rate of Change of Susceptibles in the SI Model ni, Continuous Rate of change of Infectious in the SIS Model ni, Continuous Rate of change of Susceptibles in the SIR Model ni, Continuous Rate of change of Susceptibles in the SIS Model ni, Control System Initial (Reduced) ni, Control System Input Bilinear ni, Control System Input Bilinear (Reduced) ni, Control System Input Linear ni, Control System Input Linear (Reduced) ni, Control System Matrix A (Reduced, Definition) ni, Control System Matrix B (Reduced, Definition) ni, Control System Matrix C (Reduced, Definition) ni, Control System Matrix D (Reduced, Definition) ni, Control System Matrix N (Reduced, Definition) ni, Control System Output Linear ni, Control System Output Linear (Reduced) ni, Control System Output Quadratic ni, Control System Output Quadratic (Reduced) ni, Control System State (Reduced, Definition) ni, Control Volume (Definition) ni, Coulomb Friction Of Two Particles ni, Current Density Of Electrons (Definition) ni, Current Density Of Holes (Definition) ni, Darcy Equation ni, Darcy Equation (Euler Backward) ni, Darcy Equation (Finite Volume) ni, Darwin-Howie-Whelan Equation for a strained crystal ni, Darwin-Howie-Whelan Equation for an unstrained crystal ni, Decision Variable (Definition) ni, Detailed Balance Principle ni, Dirichlet Boundary Condition ni, Dirichlet Boundary Condition For Electric Potential ni, Dirichlet Boundary Condition For Electron Fermi Potential ni, Dirichlet Boundary Condition For Hole Fermi Potential ni, Dixon Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption) ni, Dixon Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni, Dixon Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption) ni, Dixon Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption) ni, Eadie Hofstee Equation (Uni Uni Reaction without Product - Steady State Assumption) ni, Eadie Hofstee Equation (Uni Uni Reaction without Product - Irreversibility Assumption) ni, Eadie Hofstee Equation (Uni Uni Reaction without Product - Rapid Equilibrium Assumption) ni, Eadie Hofstee Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption) ni, Eadie Hofstee Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni, Eadie Hofstee Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption) ni, Eadie Hofstee Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption) ni, Electrophysiological Muscle ODE System ni, Empirical Distribution Of Individuals Formulation ni, Enzyme - Product 1 - Complex Concentration ODE (Bi Bi Reaction Ordered with single central Complex) ni, Enzyme - Product 1 - Complex Concentration ODE (Bi Bi Reaction Ordered) ni, Enzyme - Product 1 - Product 2 - Complex Concentration ODE (Bi Bi Reaction Ordered) ni, Enzyme - Product 2 - Complex Concentration ODE (Bi Bi Reaction Theorell-Chance) ni, Enzyme - Substrate - Complex Concentration ODE (Uni Uni Reaction) ni, Enzyme - Substrate 1 - Complex Concentration ODE (Bi Bi Reaction Ordered with single central Complex) ni, Enzyme - Substrate 1 - Complex Concentration ODE (Bi Bi Reaction Ordered) ni, Enzyme - Substrate 1 - Complex Concentration ODE (Bi Bi Reaction Ping Pong) ni, Enzyme - Substrate 1 - Complex Concentration ODE (Bi Bi Reaction Theorell-Chance) ni, Enzyme - Substrate 1 - Substrate 2 - Complex Concentration ODE (Bi Bi Reaction Ordered) ni, Enzyme - Substrate 1 - Substrate 2 = Enzyme - Product 1 - Product 2 - Complex Concentration ODE (Bi Bi Reaction Ordered with single central Complex) ni, Enzyme Concentration ODE (Bi Bi Reaction Ordered with single central Complex) ni, Enzyme Concentration ODE (Bi Bi Reaction Ordered) ni, Enzyme Concentration ODE (Bi Bi Reaction Ping Pong) ni, Enzyme Concentration ODE (Bi Bi Reaction Theorell-Chance) ni, Enzyme Concentration ODE (Uni Uni Reaction) ni, Enzyme Conservation ni, Equilibrium Constant (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni, Equilibrium Constant (Bi Bi Reaction Ordered - Steady State Assumption) (Definition) ni, Equilibrium Constant (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni, Equilibrium Constant (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni, Equivalance Equation Placeholder ni, Euler Backward Method ni, Euler Forward Method ni, Excess Substrate Assumption ni, Expectation Value (Quantum Density, Definition) ni, Expectation Value (Quantum State, Definition) ni, Faraday Law ni, Fick Equation ni, Finite Volume Method ni, Fourier Equation ni, Fraction Of Population Density Of Exposed Formulation ni, Fraction Of Population Density Of Infectious Formulation ni, Fraction Of Population Density Of Susceptibles Formulation ni, Free Fall Equation (Air Drag) ni, Free Fall Equation (Non-Uniform Gravitation) ni, Free Fall Equation (Vacuum) ni, Free Fall Initial Condition ni, Free Fall Terminal Velocity (Definition) ni, Free Fall Time (Definition) ni, Gamma-Gompertz–Makeham Law ni, Gated Recurrent Unit Layer ni, Gauss Law (Electric Field) ni, Gauss Law (Magnetic Field) ni, Gaussian Distribution (Definition) ni, Gompertz Law ni, Gompertz–Makeham Law ni, Gramian Generalized Controllability (Definition) ni, Gramian Generalized Observability (Definition) ni, Gramian Matrix Controllability (Definition) ni, Gramian Matrix Observability (Definition) ni, Gravitational Acceleration (Earth Surface, Definition) ni, Hanes Woolf Equation (Uni Uni Reaction without Product - Steady State Assumption) ni, Hanes Woolf Equation (Uni Uni Reaction without Product - Irreversibility Assumption) ni, Hanes Woolf Equation (Uni Uni Reaction without Product - Rapid Equilibrium Assumption) ni, Hanes Woolf Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption) ni, Hanes Woolf Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni, Hanes Woolf Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption) ni, Hanes Woolf Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption) ni, Hill-Type Two-Muscle-One-Tendon ODE System ni, Hooke Law (Linear Elasticity) ni, Hooke Law (Spring) ni, Infectious At Time Step n+1 in The SIS Model ni, Infectious At Time Step n+1 in The SIS Model with births and deaths ni, Infectious At Time Step n+1 in the Multi-Population SI Model ni, Infectious At Time Step n+1 in the Multi-Population SIR Model ni, Infectious At Time Step n+1 in the Multi-Population SIS Model ni, Infectious At Time Step n+1 in the SI Model ni, Infectious At Time Step n+1 in the SIR Model ni, Infectious At Time Step n+1 in the SIR Model with Births and Deaths ni, Inhibition Constant Product 1 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni, Inhibition Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption, Definition) ni, Inhibition Constant Product 1 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni, Inhibition Constant Product 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni, Inhibition Constant Product 2 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni, Inhibition Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption, Definition) ni, Inhibition Constant Product 2 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni, Inhibition Constant Product 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni, Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni, Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption, Definition) ni, Inhibition Constant Substrate 1 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni, Inhibition Constant Substrate 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni, Inhibition Constant Substrate 2 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni, Inhibition Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption, Definition) ni, Inhibition Constant Substrate 2 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni, Inhibition Constant Substrate 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni, Initial Classical Density ni, Initial Classical Momentum ni, Initial Classical Position ni, Initial Classical Velocity ni, Initial Condition for the Multi-Population SI Model ni, Initial Condition for the Multi-Population SIS Model ni, Initial Condition For The Discrete SIR Model with and without Births and Deaths ni, Initial Condition for the Continuous SI Model and SIS Model ni, Initial Condition for the Continuous SIR Model ni, Initial Condition for the Discrete SI Model ni, Initial Condition for the Multi-Population SIR Model ni, Initial Control State ni, Initial Control State (Reduced, Definition) ni, Initial Enzyme - Product 1 - Complex Concentration (Bi Bi Reaction Ordered - ODE Model) ni, Initial Enzyme - Product 1 - Product 2 - Complex Concentration (Bi Bi Reaction Ordered - ODE Model) ni, Initial Enzyme - Product 2 - Complex Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni, Initial Enzyme - Substrate - Complex Concentration (Uni Uni Reaction - ODE Model) ni, Initial Enzyme - Substrate 1 - Complex Concentration (Bi Bi Reaction Ordered - ODE Model) ni, Initial Enzyme - Substrate 1 - Complex Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni, Initial Enzyme - Substrate 1 - Complex Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni, Initial Enzyme - Substrate 1 - Substrate 2 - Complex Concentration (Bi Bi Reaction Ordered - ODE Model) ni, Initial Enzyme - Substrate 1 - Substrate 2 = Enzyme Product 1 - Product 2 - Complex Concentration (Bi Bi Reaction Ordered with single central Compelx - ODE Model) ni, Initial Enzyme Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni, Initial Enzyme Concentration (Bi Bi Reaction Ordered - ODE Model) ni, Initial Enzyme Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model) ni, Initial Enzyme Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni, Initial Enzyme Concentration (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model) ni, Initial Enzyme Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni, Initial Enzyme Concentration (Uni Uni Reaction - Michaelis Menten Model) ni, Initial Enzyme Concentration (Uni Uni Reaction - ODE Model) ni, Initial Inhibitor Concentration (Uni Uni Reaction) ni, Initial Intermediate - Substrate 2 - Complex Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni, Initial Intermediate Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni, Initial Number Of Infected Cities ni, Initial Product 1 Concentration (Bi Bi Reaction Ordered - ODE Model) ni, Initial Product 1 Concentration (Bi Bi Reaction Ordered with Product 1 - Michaelis Menten Model) ni, Initial Product 1 Concentration (Bi Bi Reaction Ordered without Product 1 - Michaelis Menten Model) ni, Initial Product 1 Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni, Initial Product 1 Concentration (Bi Bi Reaction Ping Pong with Product 1 - Michaelis Menten Model) ni, Initial Product 1 Concentration (Bi Bi Reaction Ping Pong without Product 1 - Michaelis Menten Model) ni, Initial Product 1 Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni, Initial Product 1 Concentration (Bi Bi Reaction Theorell-Chance with Product 1 - Michaelis Menten Model) ni, Initial Product 1 Concentration (Bi Bi Reaction Theorell-Chance without Product 1 - Michaelis Menten Model) ni, Initial Product 2 Concentration (Bi Bi Reaction Ordered - ODE Model) ni, Initial Product 2 Concentration (Bi Bi Reaction Ordered with Product 2 - Michaelis Menten Model) ni, Initial Product 2 Concentration (Bi Bi Reaction Ordered without Product 2 - Michaelis Menten Model) ni, Initial Product 2 Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model) ni, Initial Product 2 Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni, Initial Product 2 Concentration (Bi Bi Reaction Ping Pong with Product 2 - Michaelis Menten Model) ni, Initial Product 2 Concentration (Bi Bi Reaction Ping Pong without Product 2 - Michaelis Menten Model) ni, Initial Product 2 Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni, Initial Product 2 Concentration (Bi Bi Reaction Theorell-Chance with Product 2 - Michaelis Menten Model) ni, Initial Product 2 Concentration (Bi Bi Reaction Theorell-Chance without Product 2 - Michaelis Menten Model) ni, Initial Product Concentration (Uni Uni Reaction - ODE Model) ni, Initial Product Concentration (Uni Uni Reaction with Product) ni, Initial Product Concentration (Uni Uni Reaction without Product) ni, Initial Quantum Density ni, Initial Quantum State ni, Initial Substrate 1 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni, Initial Substrate 1 Concentration (Bi Bi Reaction Ordered - ODE Model) ni, Initial Substrate 1 Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model) ni, Initial Substrate 1 Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni, Initial Substrate 1 Concentration (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model) ni, Initial Substrate 1 Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni, Initial Substrate 2 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni, Initial Substrate 2 Concentration (Bi Bi Reaction Ordered - ODE Model) ni, Initial Substrate 2 Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model) ni, Initial Substrate 2 Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni, Initial Substrate 2 Concentration (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model) ni, Initial Substrate 2 Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni, Initial Substrate Concentration (Uni Uni Reaction - ODE Model) ni, Initial Substrate Concentration (Uni Uni Reaction) ni, Initial Value For Electron Scattering ni, Integral Of The Population Density Fraction Of Exposed (Initial Condition) ni, Integral Of The Population Density Fraction Of Infectious (Initial Condition) ni, Integral Of The Population Density Fraction Of Susceptibles (Initial Condition) ni, Integral Of The Total Population Density (Initial Condition) ni, Interaction Force On An Individual ni, Interaction Weight Between Individuals ni, Intermediate - Substrate 2 - Complex Concentration ODE (Bi Bi Reaction Ping Pong) ni, Intermediate Concentration ODE (Bi Bi Reaction Ping Pong) ni, Irreversibility Assumption ni, Isotropic Gaussian Function Formulation ni, Laplace Equation For The Electric Potential ni, Limiting Distribution Of Individuals Formulation ni, Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Backward, Definition) ni, Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Forward, Definition) ni, Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism with single central Complex - Forward, Definition) ni, Limiting Reaction Rate (Uni Uni Reaction - Backward, Definition) ni, Limiting Reaction Rate (Uni Uni Reaction - Forward, Definition) ni, Limiting Reaction Rate Backward (Bi Bi Reaction Ordered - Single central Complex) ni, Limiting Reaction Rate Backward (Bi Bi Reaction Ping Pong) ni, Limiting Reaction Rate Backward (Bi Bi Reaction Theorell-Chance) ni, Limiting Reaction Rate Forward (Bi Bi Reaction Ping Pong) ni, Limiting Reaction Rate Forward (Bi Bi Reaction Theorell-Chance) ni, Limiting Reaction Rate with Inhibitor (Uni Uni Reaction - Forward, Definition) ni, Line Concept ni, Line Concept Costs ni, Line Costs Computation ni, Linear Strain (Definition) ni, Lineweaver Burk Equation (Uni Uni Reaction without Product - Steady State Assumption) ni, Lineweaver Burk Equation (Uni Uni Reaction without Product - Irreversibility Assumption) ni, Lineweaver Burk Equation (Uni Uni Reaction without Product - Rapid Equilibrium Assumption) ni, Lineweaver Burk Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption) ni, Lineweaver Burk Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni, Lineweaver Burk Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption) ni, Lineweaver Burk Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption) ni, Liouville-von Neumann Equation ni, Logical Rule Extraction Formulation ni, Lorentz Force Equation (Non-Relativistic) ni, Lorentz Force Equation (Relativistic) ni, Loss Function (Definition) ni, Loss Function Minimization ni, Lumped Activation Parameter ni, Lyapunov Equation ni, Lyapunov Equation Controllability ni, Lyapunov Equation Observability ni, Lyapunov Generalized Controllability ni, Lyapunov Generalized Observability ni, Mass Action Law ni, Mass Balance Law ni, Michaelis Constant Product (Uni Uni Reaction - Steady State Assumption, Definition) ni, Michaelis Constant Product 1 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni, Michaelis Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption, Definition) ni, Michaelis Constant Product 1 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni, Michaelis Constant Product 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni, Michaelis Constant Product 2 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni, Michaelis Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption, Definition) ni, Michaelis Constant Product 2 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni, Michaelis Constant Product 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni, Michaelis Constant Substrate (Uni Uni Reaction - Irreversibility Assumption, Definition) ni, Michaelis Constant Substrate (Uni Uni Reaction - Rapid Equilibrium Assumption, Definition) ni, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption, Definition) ni, Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption, Definition) ni, Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption, Definition) ni, Michaelis Constant Substrate 1 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni, Michaelis Constant Substrate 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni, Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption, Definition) ni, Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption, Definition) ni, Michaelis Constant Substrate 2 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni, Michaelis Constant Substrate 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni, Michaelis Menten Equation (Bi Bi Reaction Ordered with Product 1 - Steady State Assumption) ni, Michaelis Menten Equation (Bi Bi Reaction Ordered with Product 1 and single central Complex - Steady State Assumption) ni, Michaelis Menten Equation (Bi Bi Reaction Ordered with Product 2 - Steady State Assumption) ni, Michaelis Menten Equation (Bi Bi Reaction Ordered with Product 2 and single central Complex - Steady State Assumption) ni, Michaelis Menten Equation (Bi Bi Reaction Ordered with Products 1 and 2 - Steady State Assumption) ni, Michaelis Menten Equation (Bi Bi Reaction Ordered with Products 1 and 2 and single central Complex - Steady State Assumption) ni, Michaelis Menten Equation (Bi Bi Reaction Ordered without Products - Steady State Assumption) ni, Michaelis Menten Equation (Bi Bi Reaction Ordered without Products and single central Complex - Steady State Assumption) ni, Michaelis Menten Equation (Bi Bi Reaction Ping Pong with Product 1 - Michaelis Menten Model - Steady State Assumption) ni, Michaelis Menten Equation (Bi Bi Reaction Ping Pong with Product 2 - Michaelis Menten Model - Steady State Assumption) ni, Michaelis Menten Equation (Bi Bi Reaction Ping Pong with Products 1 and 2 - Michaelis Menten Model - Steady State Assumption) ni, Michaelis Menten Equation (Bi Bi Reaction Ping Pong without Products - Michaelis Menten Model - Steady State Assumption) ni, Michaelis Menten Equation (Bi Bi Reaction Theorell-Chance with Product 1 - Michaelis Menten Model - Steady State Assumption) ni, Michaelis Menten Equation (Bi Bi Reaction Theorell-Chance with Product 2 - Michaelis Menten Model - Steady State Assumption) ni, Michaelis Menten Equation (Bi Bi Reaction Theorell-Chance with Products 1 and 2 - Michaelis Menten Model - Steady State Assumption) ni, Michaelis Menten Equation (Bi Bi Reaction Theorell-Chance without Products - Michaelis Menten Model - Steady State Assumption) ni, Michaelis Menten Equation (Uni Uni Reaction with Product - Steady State Assumption) ni, Michaelis Menten Equation (Uni Uni Reaction without Product - Steady State Assumption) ni, Michaelis Menten Equation (Uni Uni Reaction without Product - Irreversibility Assumption) ni, Michaelis Menten Equation (Uni Uni Reaction without Product - Rapid Equilibrium Assumption) ni, Michaelis Menten Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption) ni, Michaelis Menten Equation (Uni Uni Reaction without Product and Competitive Partial Inhibition - Steady State Assumption) ni, Michaelis Menten Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni, Michaelis Menten Equation (Uni Uni Reaction without Product and Mixed Partial Inhibition - Steady State Assumption) ni, Michaelis Menten Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption) ni, Michaelis Menten Equation (Uni Uni Reaction without Product and Non-Competitive Partial Inhibition - Steady State Assumption) ni, Michaelis Menten Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption) ni, Michaelis Menten Equation (Uni Uni Reaction without Product and Uncompetitive Partial Inhibition - Steady State Assumption) ni, Mixed Enzyme Inhibition Coupling Condition (Uni Uni Reaction) ni, Molecular Alignment ni, Molecular Orientation ni, Momentum Balance Equation ni, Monodomain Equation for Action Potential Propagation ni, Motor Neuron Pool ODE System ni, Neumann Boundary Condition ni, Neumann Boundary Condition (Stress-Free Relaxation) ni, Neumann Boundary Condition For Electric Potential ni, Neumann Boundary Condition For Electron Fermi Potential ni, Neumann Boundary Condition For Hole Fermi Potential ni, Neumann Boundary Condition For SEIR Model ni, Non-Competitive Enzyme Inhibition Coupling Condition (Uni Uni Reaction) ni, Non-Local Means ni, Nonrelativistic Approximation ni, Normal Interaction Force Of Two Particles ni, Normal Mode Coordinate (Dimensionless, Definition) ni, Normal Mode Momentum (Dimensionless, Definition) ni, Number Of Exposed Individuals Formulation ni, Number Of Individuals Tends To Infinity Assumption ni, Number Of Susceptible Individuals Formulation ni, Object Cluster Formulation ni, Object Committor Function Formulation ni, Object Commonality Formulation ni, Object Comparison Formulation ni, Object Rating Formulation ni, Object Rating Matrix Decomposition (Schur) ni, Ohm Equation ni, Optimal Control Backward ni, Optimal Control Constraint ni, Optimal Control Cost (Definition) ni, Optimal Control Final ni, Optimal Control Forward ni, Optimal Control Initial ni, Optimal Control Target (Definition) ni, Optimal Control Update ni, Overall Distribution Of Individuals Formulation ni, Pair Function Assumption ni, Passive Muscle Force (Definition) ni, Passive Tendon Force (Definition) ni, Periodic Boundary Condition For Electric Potential ni, Periodic Boundary Conditions ni, Permittivity (Relative, Definition) ni, Poisson Distribution (Definition) ni, Poisson Equation For The Electric Potential ni, Poisson Equation For The Electric Potential (Finite Volume) ni, Poisson log-Likelihood ni, Poisson-Distributed Deaths ni, Poro-Visco-Elastic (Dirichlet Boundary) ni, Poro-Visco-Elastic (Neumann Boundary) ni, Poro-Visco-Elastic Diffusion Boundary Condition ni, Poro-Visco-Elastic Diffusion Equation ni, Poro-Visco-Elastic Quasistatic Equation ni, Product 1 Concentration ODE (Bi Bi Reaction Ordered with single central Complex) ni, Product 1 Concentration ODE (Bi Bi Reaction Ordered) ni, Product 1 Concentration ODE (Bi Bi Reaction Ping Pong) ni, Product 1 Concentration ODE (Bi Bi Reaction Theorell-Chance) ni, Product 2 Concentration ODE (Bi Bi Reaction Ordered with single central Complex) ni, Product 2 Concentration ODE (Bi Bi Reaction Ordered) ni, Product 2 Concentration ODE (Bi Bi Reaction Ping Pong) ni, Product 2 Concentration ODE (Bi Bi Reaction Theorell-Chance) ni, Product Concentration ODE (Uni Uni Reaction) ni, Public Transportation Network ni, Quantum Eigen Energy (Anharmonic) ni, Quantum Eigen Energy (Harmonic) ni, Quantum Eigen Energy (Intermolecular) ni, Quantum Hamiltonian (Electric Charge) ni, Quantum Hamiltonian (Electric Dipole) ni, Quantum Hamiltonian (Electric Polarizability) ni, Quantum Hamiltonian (Linear Rotor) ni, Quantum Hamiltonian (Non-Rigid Rotor) ni, Quantum Hamiltonian (Normal Mode) ni, Quantum Hamiltonian (Normal Mode, Anharmonic) ni, Quantum Hamiltonian (Normal Mode, Harmonic) ni, Quantum Hamiltonian (Normal Mode, Intermolecular) ni, Quantum Hamiltonian (Symmetric Top) ni, Quantum Jump Operator (Definition) ni, Quantum Lindblad Equation ni, Quantum Liouville Equation ni, Quantum Momentum Operator (Definition) ni, Rapid Equilibrium Assumption ni, Rate Of Change Of Population Density Fraction Of Exposed PDE ni, Rate Of Change Of Population Density Fraction Of Infectious PDE ni, Rate Of Change Of Population Density Fraction Of Removed PDE ni, Rate Of Change Of Population Density Fraction Of Susceptibles PDE ni, Rate Of Switching Influencers Formulation ni, Relativistic Momentum (Definition) ni, Removed At Time Step n+1 in The Multi-Population Discrete Susceptible Infectious Removed Model ni, Removed At Time Step n+1 in The SIR Model ni, Removed At Time Step n+1 in the SIR Model with Births and Deaths ni, Runge–Kutta Method ni, SEIR Derivative Relation ni, Schrödinger Equation (Chebychev Polynomial) ni, Schrödinger Equation (Differencing Scheme) ni, Schrödinger Equation (Lie-Trotter) ni, Schrödinger Equation (Second Order Differencing) ni, Schrödinger Equation (Split Operator) ni, Schrödinger Equation (Strang-Marchuk) ni, Schrödinger Equation (Time Dependent) ni, Schrödinger Equation (Time Independent) ni, Schrödinger-Newton Equation ni, Second Condition For Positive Solutions In The Multi Population SIS Model ni, Second Condition For Positive Solutions In The SIR Model with Births and Deaths ni, Second Condition For Positive Solutions In The SIS Model ni, Second Condition For Positive Solutions In The SIS Model with Births and Deaths ni, Sensory Organ ni, Solar System Equations Of Motion ni, Speed Of Light (Definition) ni, Spherical Harmonics Expansion (3D) ni, Spreading Curve (Approximate, Formulation) ni, Spreading Rate (Time-dependent) Constraint ni, Stability Autonomous System ni, Steady State Assumption ni, Stokes Darcy Coupling Conditions ni, Stokes Darcy Equation (Discretized, pv) ni, Stokes Darcy Equation (Discretized, td) ni, Stokes Equation ni, Stokes Equation (Euler Backward) ni, Stokes Equation (Finite Volume) ni, Subcellular DAE System ni, Substrate 1 Concentration ODE (Bi Bi Reaction Ordered with single central Complex) ni, Substrate 1 Concentration ODE (Bi Bi Reaction Ordered) ni, Substrate 1 Concentration ODE (Bi Bi Reaction Ping Pong) ni, Substrate 1 Concentration ODE (Bi Bi Reaction Theorell-Chance) ni, Substrate 2 Concentration ODE (Bi Bi Reaction Ordered with single central Complex) ni, Substrate 2 Concentration ODE (Bi Bi Reaction Ordered) ni, Substrate 2 Concentration ODE (Bi Bi Reaction Ping Pong) ni, Substrate 2 Concentration ODE (Bi Bi Reaction Theorell-Chance) ni, Substrate Concentration ODE (Uni Uni Reaction) ni, Susceptible Cities ODE ni, Susceptible Infectious Epidemic Spreading ODE System ni, Susceptibles At Time Step n +1 in the Multi Population SI Model ni, Susceptibles At Time Step n +1 in the Multi Population SIR Model ni, Susceptibles At Time Step n +1 in the Multi Population SIS Model ni, Susceptibles At Time Step n+1 in The SI Model ni, Susceptibles At Time Step n+1 in The SIR Model ni, Susceptibles At Time Step n+1 in The SIS Model ni, Susceptibles At Time Step n+1 in The SIS Model with births and deaths ni, Susceptibles At Time Step n+1 in the SIR Model with births and deaths ni, Sylvester Equation ni, Sylvester Equation Controllability ni, Sylvester Equation Observability ni, Sylvester Generalized Controllability ni, Sylvester Generalized Observability ni, Tangential Interaction Force Of Two Particles ni, Tendon Strain (Definition) ni, Torque Of Particle ni, Total Population Density Formulation ni, Transport Equation ni, Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) Definition ni, Uni Uni Reaction ODE System ni, Uniform Gravitational Acceleration ni, Vanishing Air Density ni, Vanishing Drag Coefficient ni, Vibrational Frequency Shift (1st Order) ni, Vibrational Frequency Shift (2nd Order) ni, Weight Factor (Definition) ni, Young Modulus (Definition) ni, de Broglie Wavelength (Definition) ni
is disjoint with
Computational Task c, Mathematical Model c, Publication c, Quantity c, Quantity Kind c, Research Field c, Research Problem c, Task c

Mathematical Modelc back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathmoddb#MathematicalModel

A mathematical model for describing a part of the reality by means of abstraction and simplifying assumptions. The aim of modeling is to make a particular part or feature of the world easier to simulate, interpret and/or optimize based on existing knowledge.
is in domain of
applied by task op, approximated by model op, approximates model op, contained in model op, contains assumption op, contains boundary condition op, contains constraint condition op, contains coupling condition op, contains final condition op, contains formulation op, contains initial condition op, contains model op, discretized by model op, discretizes model op, documented in op, generalized by model op, generalizes model op, invented in op, is convex dp, is deterministic dp, is dimensionless dp, is dynamic dp, is linear dp, is space-continuous dp, is time-continuous dp, linearized by model op, linearizes model op, models op, similar to model op, studied in op, surveyed in op, used in op
is in range of
applies model op, approximated by model op, approximates model op, contained as assumption in op, contained as boundary condition in op, contained as constraint condition in op, contained as coupling condition in op, contained as final condition in op, contained as formulation in op, contained as initial condition in op, contained in model op, contains model op, discretized by model op, discretizes model op, documents op, generalized by model op, generalizes model op, invents op, linearized by model op, linearizes model op, modeled by op, similar to model op, studies op, surveys op, uses op
has members
Action Potential Propagation Model ni, Artificial Neural Network ni, Bi Bi Reaction Ordered Mechanism (ODE Model) ni, Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Product 1 (Steady State Assumption) ni, Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Product 1 and single central Complex (Steady State Assumption) ni, Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Product 2 (Steady State Assumption) ni, Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Product 2 and single central Complex (Steady State Assumption) ni, Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Products 1 and 2 (Steady State Assumption) ni, Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Products 1 and 2 and single central Complex (Steady State Assumption) ni, Bi Bi Reaction Ordered Mechanism Michaelis Menten Model without Products (Steady State Assumption) ni, Bi Bi Reaction Ordered Mechanism Michaelis Menten Model without Products and single central Complex (Steady State Assumption) ni, Bi Bi Reaction Ordered Mechanism with single central Complex (ODE Model) ni, Bi Bi Reaction Ping Pong Mechanism (ODE Model) ni, Bi Bi Reaction Ping Pong Mechanism Michaelis Menten Model with Product 1 (Steady State Assumption) ni, Bi Bi Reaction Ping Pong Mechanism Michaelis Menten Model with Product 2 (Steady State Assumption) ni, Bi Bi Reaction Ping Pong Mechanism Michaelis Menten Model with Products 1 and 2 (Steady State Assumption) ni, Bi Bi Reaction Ping Pong Mechanism Michaelis Menten Model without Products (Steady State Assumption) ni, Bi Bi Reaction Theorell-Chance Mechanism (ODE Model) ni, Bi Bi Reaction Theorell-Chance Mechanism Michaelis Menten Model with Product 1 (Steady State Assumption) ni, Bi Bi Reaction Theorell-Chance Mechanism Michaelis Menten Model with Product 2 (Steady State Assumption) ni, Bi Bi Reaction Theorell-Chance Mechanism Michaelis Menten Model with Products 1 and 2 (Steady State Assumption) ni, Bi Bi Reaction Theorell-Chance Mechanism Michaelis Menten Model without Products (Steady State Assumption) ni, Charge Transport Model ni, Classical Brownian Model ni, Classical Dynamics Model ni, Classical Fokker Planck Model ni, Classical Langevin Model ni, Continuous Susceptible Infectious Model ni, Continuous Susceptible Infectious Removed Model ni, Continuous Susceptible Infectious Susceptible Model ni, Control System Model ni, Control System Model (Bilinear) ni, Control System Model (Linear) ni, Darcy Model ni, Darcy Model (Discretized) ni, Diffusion Model ni, Discrete Element Method ni, Discrete Susceptible Infectious Model ni, Discrete Susceptible Infectious Removed Model ni, Discrete Susceptible Infectious Susceptible Model ni, Drift-Diffusion Model ni, Dynamical Electron Scattering Model ni, Electron Shuttling Model ni, Electrophysiological Muscle Model ni, Feedforward Neural Network ni, Free Fall Model (Air Drag) ni, Free Fall Model (Non-Uniform Gravitation) ni, Free Fall Model (Vacuum) ni, Gamma-Gompertz-Makeham Model ni, Gaussian Noise Model ni, Heat Conduction Model ni, Hill-Type Two-Muscle-One-Tendon Model ni, Linear Discrete Element Method ni, Linear Rotor ni, Linear Rotor (Apolar) ni, Linear Rotor (Combined) ni, Linear Rotor (Non-Rigid) ni, Linear Rotor (Polar) ni, Lorentz Force Model (Non-Relativistic) ni, Lorentz Force Model (Relativistic) ni, Loss Function ni, Maxwell Equations Model ni, Motor Neuron Pool Model ni, Multi-Population Discrete Susceptible Infectious Model ni, Multi-Population Discrete Susceptible Infectious Removed Model ni, Multi-Population Discrete Susceptible Infectious Susceptible Model ni, Multipolar Expansion Model (3D) ni, Normal Modes ni, Normal Modes (Anharmonic) ni, Normal Modes (Harmonic) ni, Normal Modes (Intermolecular) ni, Object Comparison Model ni, Opinion Model With Influencers And Media ni, PDE SEIR Model ni, Partial Mean Field Opinion Model ni, Poro-Visco-Elastic Model ni, Quantum Classical Model ni, Quantum Model (Closed System) ni, Quantum Model (Open System) ni, Recurrent Neural Network Surrogate for Discrete Element Method ni, Scharfetter-Gummel Scheme ni, Sensory Organ Model ni, Solar System Model ni, Stokes Darcy Model ni, Stokes Darcy Model (Discretized) ni, Stokes Model ni, Stokes Model (Discretized) ni, Subcellular Model ni, Susceptible Infectious Epidemic Spreading Model ni, Susceptible Infectious Removed Model with Births and Deaths ni, Susceptible Infectious Susceptible Model with Births and Deaths ni, Symmetric Top (Combined) ni, Transport Model ni, Uni Uni Reaction (Eadie Hofstee Model without Product - Irreversibility Assumption) ni, Uni Uni Reaction (Eadie Hofstee Model without Product - Rapid Equilibrium Assumption) ni, Uni Uni Reaction (Eadie Hofstee Model without Product - Steady State Assumption) ni, Uni Uni Reaction (Hanes Woolf Model without Product - Irreversibility Assumption) ni, Uni Uni Reaction (Hanes Woolf Model without Product - Rapid Equilibrium Assumption) ni, Uni Uni Reaction (Hanes Woolf Model without Product - Steady State Assumption) ni, Uni Uni Reaction (Lineweaver Burk Model without Product - Irreversibility Assumption) ni, Uni Uni Reaction (Lineweaver Burk Model without Product - Rapid Equilibrium Assumption) ni, Uni Uni Reaction (Lineweaver Burk Model without Product - Steady State Assumption) ni, Uni Uni Reaction (Michaelis Menten Model with Product - Steady State Assumption) ni, Uni Uni Reaction (Michaelis Menten Model without Product - Irreversibility Assumption) ni, Uni Uni Reaction (Michaelis Menten Model without Product - Rapid Equilibrium Assumption) ni, Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni, Uni Uni Reaction (ODE Model) ni, Uni Uni Reaction Competitive Complete Inhibition (Dixon Model without Product - Steady State Assumption) ni, Uni Uni Reaction Competitive Complete Inhibition (Eadie Hofstee Model without Product - Steady State Assumption) ni, Uni Uni Reaction Competitive Complete Inhibition (Hanes Woolf Model without Product - Steady State Assumption) ni, Uni Uni Reaction Competitive Complete Inhibition (Lineweaver Burk Model without Product - Steady State Assumption) ni, Uni Uni Reaction Competitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni, Uni Uni Reaction Competitive Partial Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni, Uni Uni Reaction Mixed Complete Inhibition (Dixon Model without Product - Steady State Assumption) ni, Uni Uni Reaction Mixed Complete Inhibition (Eadie Hofstee Model without Product - Steady State Assumption) ni, Uni Uni Reaction Mixed Complete Inhibition (Hanes Woolf Model without Product - Steady State Assumption) ni, Uni Uni Reaction Mixed Complete Inhibition (Lineweaver Burk Model without Product - Steady State Assumption) ni, Uni Uni Reaction Mixed Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni, Uni Uni Reaction Mixed Partial Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni, Uni Uni Reaction Non-Competitive Complete Inhibition (Dixon Model without Product - Steady State Assumption) ni, Uni Uni Reaction Non-Competitive Complete Inhibition (Eadie Hofstee Model without Product - Steady State Assumption) ni, Uni Uni Reaction Non-Competitive Complete Inhibition (Hanes Woolf Model without Product - Steady State Assumption) ni, Uni Uni Reaction Non-Competitive Complete Inhibition (Lineweaver Burk Model without Product - Steady State Assumption) ni, Uni Uni Reaction Non-Competitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni, Uni Uni Reaction Non-Competitive Partial Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni, Uni Uni Reaction Uncompetitive Complete Inhibition (Dixon Model without Product - Steady State Assumption) ni, Uni Uni Reaction Uncompetitive Complete Inhibition (Eadie Hofstee Model without Product - Steady State Assumption) ni, Uni Uni Reaction Uncompetitive Complete Inhibition (Hanes Woolf Model without Product - Steady State Assumption) ni, Uni Uni Reaction Uncompetitive Complete Inhibition (Lineweaver Burk Model without Product - Steady State Assumption) ni, Uni Uni Reaction Uncompetitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni, Uni Uni Reaction Uncompetitive Partial Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni, van Roosbroeck Model ni
is disjoint with
Computational Task c, Mathematical Formulation c, Publication c, Quantity c, Quantity Kind c, Research Field c, Research Problem c, Task c

Publicationc back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathmoddb#Publication

publication that reports original empirical and theoretical work in the sciences
is in domain of
documents op, invents op, studies op, surveys op, uses op
is in range of
documented in op, invented in op, studied in op, surveyed in op, used in op
has members
Allen (1993) Some Discrete-Time SI, SIR and SIS Epidemic Models ni, Bisswanger (2017) Enzyme Kinetics ni, Briggs (1925) A note on the kinetics of enzyme action ni, Cundall (1979) A discrete numerical model for granular assemblies ni, Eadie (1942) The Inhibition of Cholinesterase by Physostigmine and Prostigmine ni, Ermoneit (2023) Optimal control of conveyor-mode spin-qubit shuttling in a Si/SiGe quantum bus in the presence of charged defects ni, Gattermann (2017) Line pool generation ni, Hanes (1932) Studies on plant amylases: The effect of starch concentration upon the velocity of hydrolysis by the amylase of germinated barley ni, Helfmann (2023) Modelling opinion dynamics under the impact of influencer and media strategies ni, Hofstee (1959) Non-inverted versus inverted plots in enzyme kinetics ni, Homs-Pons (2024) Coupled simulations and parameter inversion for neural system and electrophysiological muscle models ni, Jahnke (2022) Efficient Numerical Simulation of Soil-Tool Interaction ni, Koprucki (2017) Numerical methods for drift-diffusion models ni, Kostré (2022) Understanding the romanization spreading on historical interregional networks in Northern Tunisia ni, Leskovac (2003) Comprehensive Enzyme Kinetics ni, Lineweaver (1934) The Determination of Enzyme Dissociation Constants ni, Michaelis (1913) Die Kinetik der Invertinwirkung ni, Oosterhout (2024) Finite-strain poro-visco-elasticity with degenerate mobility ni, Slyke (1914) The mode of action of urease and of enzymes in general ni, Suan (2010) Kinetic and reactor modelling of lipases catalyzed (R,S)-1-phenylethanol resolution ni, Sylvester (1884) Sur léquations en matrices px = xq ni, Weber (2022) The Mathematics of Comparing Objects ni
is disjoint with
Computational Task c, Mathematical Formulation c, Mathematical Model c, Quantity c, Quantity Kind c, Research Field c, Research Problem c, Task c

Quantityc back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathmoddb#Quantity

A quantity is a property of a system that can be measured or obtained from calculation/simulation. Can be a scalar, a vector, a matrix or a higher-order tensor. The overarching, abstract quantity in the QuantityKind class should be referenced if possible/applicable.
is in domain of
approximated by quantity op, approximates quantity op, contained as constant in op, contained as input in op, contained as objective in op, contained as output in op, contained as parameter in op, contained in formulation op, defined by op, documented in op, generalized by quantity op, generalizes quantity op, invented in op, is dimensionless dp, is linear dp, linearized by quantity op, linearizes quantity op, nondimensionalized by quantity op, nondimensionalizes quantity op, similar to quantity op, studied in op, surveyed in op, used in op
is in range of
approximated by quantity op, approximates quantity op, contains constant op, contains input op, contains objective op, contains output op, contains parameter op, contains quantity op, defines op, documents op, generalized by quantity op, generalizes quantity op, invents op, linearized by quantity op, linearizes quantity op, nondimensionalized by quantity op, nondimensionalizes quantity op, similar to quantity op, studies op, surveys op, uses op
has members
Active Contractile Force ni, Age Of An Individual ni, Allee Threshold ni, Amplitude Of Electron Wave ni, Anharmonicity Constant ni, Applied External Voltage ni, Asymptomatic Infection Rate ni, Asymptomatic Recovery Rate ni, Attraction Force At Opinion ni, Average Opinion Of Followers Of Influencers ni, Average Opinion Of Followers Of Influencers In The Partial Mean Field Model ni, Average Opinion Of Followers Of Media ni, Average Opinion Of Followers Of Media In The Partial Mean Field Model ni, Band Edge Energy For Conduction Band ni, Band Edge Energy For Valence Band ni, Beavers-Joseph Coefficient ni, Between Population Contact Rate ni, Birth Rate ni, Boltzmann Constant ni, Boolean Ring ni, Center Of Province ni, Centrifugal Distortion Constant ni, Change In Length ni, Chemical Potential ni, Classical Acceleration ni, Classical Density (Phase Space) ni, Classical Force ni, Classical Hamilton Function ni, Classical Momentum ni, Classical Position ni, Classical Velocity ni, Coefficient Scaling Infectious To Exposed ni, Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni, Complexed Enzyme Concentration ni, Contact Network ni, Contact Network (Time-dependent) ni, Contact Rate ni, Contact Rate Between Two Groups ni, Control System Duration ni, Control System Initial ni, Control System Input ni, Control System Lagrange Multiplier ni, Control System Matrix A ni, Control System Matrix A (Reduced) ni, Control System Matrix B ni, Control System Matrix B (Reduced) ni, Control System Matrix C ni, Control System Matrix C (Reduced) ni, Control System Matrix D ni, Control System Matrix D (Reduced) ni, Control System Matrix N ni, Control System Matrix N (Reduced) ni, Control System Output ni, Control System State ni, Control System State (Reduced) ni, Control Volume ni, Coriolis Coupling Constant ni, Costs of Line Concept ni, Costs per Unit ni, Coupling Current ni, Cross Section ni, Current Density ni, Current Density Of Electrons ni, Current Density Of Holes ni, Current Procedural Terminology ni, Death Count ni, Decision Variable ni, Density Fraction Coefficient ni, Density Of Air ni, Density Of Electrons ni, Density Of Holes ni, Density Of States For Conduction Band ni, Density Of States For Valence Band ni, Diffusion Coefficient ni, Diffusion Coefficient for SEIR Model ni, Diffusion Flux ni, Dirac Delta Distribution ni, Displacement ni, Displacement Muscle Tendon ni, Displacement Of Atoms ni, Dissociation Constant ni, Doping Profile ni, Drag Coefficient ni, Drift (Velocity) ni, Duration ni, Duration per Unit ni, Earth Mass ni, Earth Radius ni, Effective Conductivity ni, Effective Mass ni, Effective Mass (Solid-State Physics) ni, Effective Mass (Spring-Mass System) ni, Eigenstress Of Crystal ni, Elastic Stiffness Tensor ni, Electric Charge Density ni, Electric Constant ni, Electric Current Density ni, Electric Potential ni, Electric Potential Fourier Coefficients ni, Electrode Interfaces ni, Electron Mass ni, Elementary Charge ni, Empirical Distribution Of Individuals ni, Enzyme - Product 1 - Product 2 Complex Concentration ni, Enzyme - Product 1 Complex Concentration ni, Enzyme - Product 2 Complex Concentration ni, Enzyme - Substrate 1 - Substrate 2 = Enzyme - Product 1 - Product 2 Complex Concentration ni, Enzyme - Substrate 1 - Substrate 2 Complex Concentration ni, Enzyme - Substrate 1 Complex Concentration ni, Enzyme Concentration ni, Enzyme-Substrate Complex Concentration ni, Equilibrium Constant ni, Equilibrium Constant (Bi Bi Reaction Ordered - Steady State Assumption) ni, Euler Number ni, Excitation Error ni, Expectation Value (Quantum Density) ni, Expectation Value (Quantum State) ni, Exposure Of An Individual ni, External Chemical Potential ni, External Force Density ni, Extrinsic Mortality ni, Fermi Potential For Electrons ni, Fermi Potential For Holes ni, Fiber Contraction Velocity ni, Fiber Stretch ni, Fixed Costs ni, Fluid Density ni, Fluid Dynamic Viscosity (Free Flow) ni, Fluid Dynamic Viscosity (Porous Medium) ni, Fluid Intrinsic Permeability (Porous Medium) ni, Fluid Kinematic Viscosity (Free Flow) ni, Fluid Pressure (Free Flow) ni, Fluid Pressure (Porous Medium) ni, Fluid Velocity (Free Flow) ni, Fluid Velocity (Porous Medium) ni, Fluid Viscous Stress ni, Flux Of Electrons ni, Flux Of Holes ni, Force Constant (Anharmonic) ni, Force Constant (Harmonic) ni, Force Density ni, Fraction Of Population Density Of Exposed ni, Fraction Of Population Density Of Infectious ni, Fraction Of Population Density Of Removed ni, Fraction Of Population Density Of Susceptibles ni, Free Energy Density ni, Free Fall Height ni, Free Fall Impact Time ni, Free Fall Impact Velocity ni, Free Fall Initial Height ni, Free Fall Initial Velocity ni, Free Fall Mass ni, Free Fall Terminal Velocity ni, Free Fall Time ni, Free Fall Velocity ni, Friction Coefficient ni, Gaussian Distribution ni, Generic Product Identifier ni, Gramian Generalized Controllability ni, Gramian Generalized Observability ni, Gramian Matrix ni, Gramian Matrix Controllability ni, Gramian Matrix Observability ni, Graph Type Identifier ni, Gravitational Acceleration (Earth Surface) ni, Gravitational Constant ni, Gröbner Basis ni, Hankel Singular Value ni, Heat Flux ni, Heterogeneity of Death Rate ni, Hydraulic Conductivity ni, Hyperstress Potential ni, Ideal ni, Individual Relationship Matrix ni, Inertia Parameter For Opinion Changes Of Influencers ni, Inertia Parameter For Opinion Changes Of Media ni, Infected Recovery Rate ni, Infectious ni, Influencer Individual Matrix ni, Inhibition Constant ni, Inhibition Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni, Inhibition Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption) ni, Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni, Inhibition Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption) ni, Inhibitor Concentration ni, Initial Control State (Reduced) ni, Initial Reaction Rate ni, Interaction Force ni, Interaction Weight ni, Intermediate - Substrate 2 Complex Concentration ni, Intermediate Concentration ni, Intermolecular Potential ni, International Classification of Diseases - 9 ni, Ion Current ni, Isotropic Gaussian Function ni, Lagrange Multiplier ni, Length Of Unit Cell ni, Level Of Mortality ni, Likelihood Value ni, Limiting Distribution Of Individuals ni, Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Backward) ni, Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Forward) ni, Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism with single central Complex - Forward) ni, Limiting Reaction Rate (Uni Uni Reaction - Backward) ni, Limiting Reaction Rate (Uni Uni Reaction - Forward) ni, Limiting Reaction Rate with Inhibitor (Uni Uni Reaction - Forward) ni, Linear Strain ni, Link Recommendation Function ni, Loss Function ni, MOR Transformation Matrix ni, Magnetic Constant ni, Material Density ni, Material Point Acceleration ni, Material Point Displacement ni, Material Point Velocity ni, Maximal Object Descriptiveness Rating ni, Maximum Isometric Muscle Force ni, Mechanical Deformation (Boundary Value) ni, Medium Follower Matrix ni, Medium Influencer Fraction ni, Medium Influencer Fraction Limit ni, Membrane Capacitance ni, Membrane Potential ni, Michaelis Constant ni, Michaelis Constant Product (Uni Uni Reaction - Steady State Assumption) ni, Michaelis Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni, Michaelis Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption) ni, Michaelis Constant Substrate (Uni Uni Reaction - Irreversibility Assumption) ni, Michaelis Constant Substrate (Uni Uni Reaction - Rapid Equilibrium Assumption) ni, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni, Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni, Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption) ni, Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption) ni, Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption) ni, Mobility Of Electrons ni, Mobility Of Holes ni, Molecularity ni, Muscle Contraction Velocity ni, Muscle Length ni, Muscle Spindle Firing Rate ni, Neural Firing Rate ni, Neural Input ni, Noise Strength ni, Normal Mode Coordinate ni, Normal Mode Coordinate (Dimensionless) ni, Normal Mode Momentum ni, Normal Mode Momentum (Dimensionless) ni, Normal Stress ni, Number Of Exposed Individuals ni, Number Of Infected Cities ni, Number Of Infectious Individuals ni, Number Of Occurrences ni, Number Of Removed Individuals ni, Number Of Susceptible Cities ni, Number Of Susceptible Individuals ni, Number of Cities ni, Number of Object Properties ni, Number of Objects ni, Number of Particles ni, Number of Regions ni, Number of Time Points ni, Object Cluster Matrix ni, Object Committor Functions ni, Object Commonality Matrix ni, Object Property ni, Object Rating Matrix ni, Opinion ni, Opinion Vector of Individuals ni, Opinion Vector of Influencers ni, Opinion Vector of Media ni, Optimal Control Cost ni, Optimal Control Penalty Factor ni, Optimal Control Target ni, Origin Destination Data ni, Orthogonal Matrix ni, Overall Distribution Of Individuals ni, PTN Line ni, Pair Function ni, Parameter To Scale Attractive Force From Influencers ni, Parameter To Scale Attractive Force From Media ni, Parameter To Scale Attractive Force From Other Individuals ni, Particle Flux Density ni, Particle Number Density ni, Passive Muscle Force ni, Passive Muscle Strain ni, Passive Tendon Force ni, Period Length ni, Permeability (Vacuum) ni, Permittivity (Dielectric) ni, Permittivity (Relative) ni, Permittivity (Vacuum) ni, Pi Number ni, Planck Constant ni, Poisson Distribution ni, Population Density ni, Power Set ni, Probability Distribution ni, Product 1 Concentration ni, Product 2 Concentration ni, Product Concentration ni, Proton Mass ni, Quantum Angular Momentum Operator ni, Quantum Damping Rate ni, Quantum Density Operator ni, Quantum Eigen Energy ni, Quantum Hamiltonian Operator ni, Quantum Jump Operator ni, Quantum Kinetic Operator ni, Quantum Mechanical Operator ni, Quantum Momentum Operator ni, Quantum Number ni, Quantum Potential Operator ni, Quantum State Vector ni, Quantum State Vector (Dynamic) ni, Quantum State Vector (Stationary) ni, Rate Of Aging ni, Rate Of Becoming Infectious ni, Rate Of Change Of Susceptible Cities ni, Rate Of Switching Influencers ni, Reaction Rate ni, Reaction Rate Constant ni, Reaction Rate of Enzyme ni, Reaction Rate of Enzyme - Product 1 - Product 2 Complex ni, Reaction Rate of Enzyme - Product 1 Complex ni, Reaction Rate of Enzyme - Product 2 Complex ni, Reaction Rate of Enzyme - Substrate 1 - Substrate 2 = Enzyme - Product 1 - Product 2 Complex ni, Reaction Rate of Enzyme - Substrate 1 - Substrate 2 Complex ni, Reaction Rate of Enzyme - Substrate 1 Complex ni, Reaction Rate of Intermediate ni, Reaction Rate of Intermediate - Substrate 2 Complex ni, Reaction Rate of Product 1 ni, Reaction Rate of Product 2 ni, Reaction Rate of Substrate 1 ni, Reaction Rate of Substrate 2 ni, Reciprocal Lattice ni, Reciprocal Lattice Vectors ni, Recombination Of Electron Hole Pairs ni, Recovery Rate ni, Region ni, Region Connectivity ni, Relative Removal Rate ni, Relativistic Momentum ni, Removed ni, Risk Of Death ni, Romanized Cities Vector ni, Rotational Constant ni, Scaling Parameter For Switching Influencers ni, Second Eigenvalue of Orthogonal Matrix ni, Sensory Organ Current ni, Spatial Variable ni, Speed Of Light ni, Spreading Curve (Approximate) ni, Spreading Rate (Time-dependent) ni, Spring Constant ni, Stress Free Muscle Length ni, Stress Free Tendon Length ni, Stress Of Crystal ni, Stress Tensor (Cauchy) ni, Stress Tensor (Piola-Kirchhoff) ni, Substrate 1 Concentration ni, Substrate 2 Concentration ni, Substrate Concentration ni, Surface Force Density ni, Susceptibles ni, Symptomatic Infection Rate ni, Tendon Length ni, Tendon Strain ni, Thermal Conductivity ni, Time Point ni, Time Step ni, Total Number Of Individuals ni, Total Population Density ni, Total Population Size ni, Traffic Load ni, Transmembrane Potential ni, Turn Over Time ni, Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni, Unit Normal Vector ni, Unit Tangent Vector ni, Unknown Matrix ni, Upper-Triangular Matrix ni, Vibration Frequency (Anharmonic) ni, Vibration Frequency (Harmonic) ni, Viscous Dissipation Potential ni, Wave Vector of an Electron ni, Weight Factor ni, White Noise ni, Wiener Process ni, Young Modulus ni, de Broglie Wavelength ni
is disjoint with
Computational Task c, Mathematical Formulation c, Mathematical Model c, Publication c, Quantity Kind c, Research Field c, Research Problem c, Task c

Quantity Kindc back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantityKind

The kind of quantity, e.g. the abstract, generalized concept of a quantity. Typically, it could be chosen from an established, controlled vocabulary of quantityKinds, such as QUDT, IEC, .... Note that the kind of a quantity cannot be generalized by another (kind of a) quantity.
is in domain of
contained as constant in op, contained as input in op, contained as objective in op, contained as output in op, contained as parameter in op, contained in formulation op, defined by op, documented in op, generalizes quantity op, invented in op, is dimensionless dp, nondimensionalized by quantity op, nondimensionalizes quantity op, similar to quantity op, studied in op, surveyed in op, used in op
is in range of
contains constant op, contains input op, contains objective op, contains output op, contains parameter op, contains quantity op, defines op, documents op, generalized by quantity op, invents op, nondimensionalized by quantity op, nondimensionalizes quantity op, similar to quantity op, studies op, surveys op, uses op
has members
Acceleration ni, Angular Momentum ni, Area ni, Azimuthal Angle ni, Boolean Variable ni, Complex Number (Dimensionless) ni, Concentration ni, Costs ni, Density ni, Electric Capacitance ni, Electric Charge ni, Electric Conductivity ni, Electric Current ni, Electric Dipole Moment ni, Electric Field ni, Electric Polarizability ni, Energy ni, Expectation Value ni, Force ni, Frequency ni, Integer Number (Dimensionless) ni, Length ni, Magnetic Field ni, Mass ni, Mechanical Deformation ni, Mechanical Strain ni, Mechanical Stress ni, Momentum ni, Number (Dimensionless) ni, Object ni, Polar Angle ni, Pressure ni, Proton Electron Mass Ratio ni, Radius ni, Rate ni, Real Number (Dimensionless) ni, Temperature ni, Time ni, Torque ni, Transport Route ni, Variance ni, Velocity ni, Viscosity ni, Voltage ni
is disjoint with
Computational Task c, Mathematical Formulation c, Mathematical Model c, Publication c, Quantity c, Research Field c, Research Problem c, Task c

Research Fieldc back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathmoddb#ResearchField

A field of research (or academic discipline), e.g. Arts & Humanities, Life Sciences & Biomedicine, Physical & Natural Sciences or Engineering.
is in domain of
contains problem op, documented in op, generalized by field op, generalizes field op, invented in op, similar to field op, studied in op, surveyed in op, used in op
is in range of
contained in field op, documents op, generalized by field op, generalizes field op, invents op, similar to field op, studies op, surveys op, uses op
has members
Archaeology ni, Astronomy ni, Biology ni, Biomechanics ni, Biophysics ni, Celestial Mechanics ni, Chemical Reaction Kinetics ni, Civil Engineering ni, Classical Mechanics ni, Computational Social Science ni, Continuum Mechanics ni, Demography ni, Egyptology ni, Electrodynamics ni, Electromagnetism ni, Enzyme Kinetics ni, Epidemiology ni, Medical Imaging ni, Molecular Physics ni, Optimization in Public Transportation ni, Physical Chemistry ni, Pomology ni, Roman Archaeology ni, Semiconductor Physics ni, Statistics ni, Transmission Electron Microscopy ni, Transportation Planning ni
is disjoint with
Computational Task c, Mathematical Formulation c, Mathematical Model c, Publication c, Quantity c, Quantity Kind c, Research Problem c, Task c

Research Problemc back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathmoddb#ResearchProblem

A research problem (or research question) to be investigated, typically from a scientific or engineering application, i.e. a specific issue or gap in existing knowledge that you aim to address in your research.
is in domain of
contained in field op, documented in op, generalized by problem op, generalizes problem op, invented in op, modeled by op, similar to problem op, studied in op, surveyed in op, used in op
is in range of
contains problem op, documents op, generalized by problem op, generalizes problem op, invents op, models op, similar to problem op, studies op, surveys op, uses op
has members
Bi Bi Reaction ni, Bi Bi Reaction following Ordered Mechanism ni, Bi Bi Reaction following Ordered Mechanism with single central complex ni, Bi Bi Reaction following Ping Pong Mechanism ni, Bi Bi Reaction following Theorell-Chance Mechanism ni, Charge Transport ni, Current flow in semiconductor devices ni, Efficient Numerical Simulation of Soil-Tool Interaction ni, Electromagnetic Fields And Waves ni, Flow in porous media ni, Free flow coupled to porous media flow ni, Free flow of an incompressible fluid ni, Gravitational Effects On Fruit ni, Heat Transport ni, Identify destruction rules in ancient egyptian objects ni, Image Denoising ni, Imaging of nanostructures ni, Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Product 1 ni, Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Product 1 and single central Complex ni, Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Product 2 ni, Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Product 2 and single central Complex ni, Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Products 1 and 2 ni, Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Products 1 and 2 and single central Complex ni, Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism without Products ni, Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism without Products and single central Complex ni, Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism with Product 1 ni, Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism with Product 2 ni, Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism with Products 1 and 2 ni, Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism without Products ni, Initial Reaction Rate of Bi Bi Reaction following Theorell-Chance Mechanism with Product 1 ni, Initial Reaction Rate of Bi Bi Reaction following Theorell-Chance Mechanism with Product 2 ni, Initial Reaction Rate of Bi Bi Reaction following Theorell-Chance Mechanism without Products ni, Initial Reaction Rate of Bi Bi Reaction following Theorell-Chance Mechanism withs Product 1 and 2 ni, Initial Reaction Rate of Uni Uni Reaction with Product ni, Initial Reaction Rate of Uni Uni Reaction without Product ni, Initial Reaction Rate of Uni Uni Reaction without Product and Competitive Complete Inhibition ni, Initial Reaction Rate of Uni Uni Reaction without Product and Competitive Partial Inhibition ni, Initial Reaction Rate of Uni Uni Reaction without Product and Mixed Complete Inhibition ni, Initial Reaction Rate of Uni Uni Reaction without Product and Mixed Partial Inhibition ni, Initial Reaction Rate of Uni Uni Reaction without Product and Non-Competitive Complete Inhibition ni, Initial Reaction Rate of Uni Uni Reaction without Product and Non-Competitive Partial Inhibition ni, Initial Reaction Rate of Uni Uni Reaction without Product and Uncompetitive Complete Inhibition ni, Initial Reaction Rate of Uni Uni Reaction without Product and Uncompetitive Partial Inhibition ni, Molecular Dynamics ni, Molecular Reaction Dynamics ni, Molecular Rotation ni, Molecular Spectroscopy ni, Molecular Spectroscopy (Transient) ni, Molecular Spectrosopy (Stationary) ni, Molecular Vibration ni, Mortality Modeling ni, Muscle Movement ni, Opinion Dynamics ni, Particles In Electromagnetic Fields ni, Poro-Visco-Elastic Evolution ni, Romanization Spreading in Northern Tunesia ni, Solar System Mechanics ni, Sort ancient Egyptian Objects ni, Species Transport ni, Spin Qbit Shuttling ni, Spreading of Infectious Diseases ni, Transport of Matter ni, Uni Uni Reaction ni, Uni Uni Reaction with Competitive Complete Inhibition ni, Uni Uni Reaction with Competitive Partial Inhibition ni, Uni Uni Reaction with Mixed Complete Inhibition ni, Uni Uni Reaction with Mixed Partial Inhibition ni, Uni Uni Reaction with Non-Competitive Complete Inhibition ni, Uni Uni Reaction with Non-Competitive Partial Inhibition ni, Uni Uni Reaction with Reversible Complete Inhibition ni, Uni Uni Reaction with Reversible Partial Inhibition ni, Uni Uni Reaction with Uncompetitive Complete Inhibition ni, Uni Uni Reaction with Uncompetitive Partial Inhibition ni
is disjoint with
Computational Task c, Mathematical Formulation c, Mathematical Model c, Publication c, Quantity c, Quantity Kind c, Research Field c, Task c

Taskc back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathmoddb#Task

A specific task associated with a mathematical model. The subclasses of this superclass should reflect their differences, e.g. a computational task or a task of doing a mathematical analysis (the latter is not yet implemented).
has sub-classes
Computational Task c
is disjoint with
Mathematical Formulation c, Mathematical Model c, Publication c, Quantity c, Quantity Kind c, Research Field c, Research Problem c

Object Properties

applied byop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#appliedBy

has sub-properties
applied by task op
is inverse of
applies op

applied by taskop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#appliedByTask

A mathematical model is applied (used) by a computational task
has super-properties
applied by op
has domain
Mathematical Model c
has range
Computational Task c
is inverse of
applies model op

appliesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#applies

has sub-properties
applies model op
is inverse of
applied by op

applies modelop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#appliesModel

A computational task applies (uses) a mathematical model
has super-properties
applies op
has domain
Computational Task c
has range
Mathematical Model c
is inverse of
applied by task op

approximated byop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#approximatedBy

has characteristics: transitive

has sub-properties
approximated by formulation op, approximated by model op, approximated by quantity op, approximated by task op
is inverse of
approximates op

approximated by formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#approximatedByFormulation

A mathematical formulation (e.g. equation) is approximated by another mathematical formulation

has characteristics: transitive

has super-properties
approximated by op
has domain
Mathematical Formulation c
has range
Mathematical Formulation c
is inverse of
approximates formulation op

approximated by modelop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#approximatedByModel

A mathematical model is approximated by another mathematical model

has characteristics: transitive

has super-properties
approximated by op
has domain
Mathematical Model c
has range
Mathematical Model c
is inverse of
approximates model op

approximated by quantityop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#approximatedByQuantity

A (physical or other) quantity is approximated by another quantity

has characteristics: transitive

has super-properties
approximated by op
has domain
Quantity c
has range
Quantity c
is inverse of
approximates quantity op

approximated by taskop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#approximatedByTask

A computational task is approximated by another computational task

has characteristics: transitive

has super-properties
approximated by op
has domain
Computational Task c
has range
Computational Task c
is inverse of
approximates task op

approximatesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#approximates

has characteristics: transitive

has sub-properties
approximates formulation op, approximates model op, approximates quantity op, approximates task op
is inverse of
approximated by op

approximates formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#approximatesFormulation

A mathematical formulation (e.g. equation) approximates another mathematical formulation

has characteristics: transitive

has super-properties
approximates op
has domain
Mathematical Formulation c
has range
Mathematical Formulation c
is inverse of
approximated by formulation op

approximates modelop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#approximatesModel

A mathematical model approximates another mathematical model

has characteristics: transitive

has super-properties
approximates op
has domain
Mathematical Model c
has range
Mathematical Model c
is inverse of
approximated by model op

approximates quantityop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#approximatesQuantity

A (physical or other) quantity approximates another quantity

has characteristics: transitive

has super-properties
approximates op
has domain
Quantity c
has range
Quantity c
is inverse of
approximated by quantity op

approximates taskop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#approximatesTask

A computational task approximates another computational task

has characteristics: transitive

has super-properties
approximates op
has domain
Computational Task c
has range
Computational Task c
is inverse of
approximated by task op

contained as assumption inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedAsAssumptionIn

Assumptions in a mathematical model|task|formulation are the conditions that must be met for the mathematical model|task|formulation to be valid.
has super-properties
contained in op
has domain
Mathematical Formulation c
has range
Computational Task c or Mathematical Formulation c or Mathematical Model c
is inverse of
contains assumption op

contained as boundary condition inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedAsBoundaryConditionIn

In the study of differential equations, a boundary-value problem is a differential equation subjected to constraints called boundary conditions.[1] A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions.
has super-properties
contained in op
has domain
Mathematical Formulation c
has range
Computational Task c or Mathematical Formulation c or Mathematical Model c
is inverse of
contains boundary condition op

contained as constant inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedAsConstantIn

This property serves to indicate that a certain quantity is considered as a constant in a computational task.
has super-properties
contained in op
has domain
Quantity c or Quantity Kind c
has range
Computational Task c or Mathematical Formulation c
is inverse of
contains constant op

contained as constraint condition inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedAsConstraintConditionIn

Solutions to a computational task or a mathematical formulation or a mathematical model are subject to a constraint which is expressed as a mathematical formulation, i.e., an equation or an inequality
has super-properties
contained in op
has domain
Mathematical Formulation c
has range
Computational Task c or Mathematical Formulation c or Mathematical Model c
is inverse of
contains constraint condition op

contained as coupling condition inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedAsCouplingConditionIn

Mathematical formulation, i.e., typically an equation, serving to model the interaction of two or more (sub-)systems that are interacting with each other
has super-properties
contained in op
has domain
Mathematical Formulation c
has range
Computational Task c or Mathematical Formulation c or Mathematical Model c
is inverse of
contains coupling condition op

contained as final condition inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedAsFinalConditionIn

Similar to initial conditions. Sometimes used in the context of optimal control
has super-properties
contained in op
has domain
Mathematical Formulation c
has range
Computational Task c or Mathematical Formulation c or Mathematical Model c
is inverse of
contains final condition op

contained as formulation inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedAsFormulationIn

use this property to denote that a mathematical formulation, e.g. an equation, is contained in a (single or coupled) model or formulation or task, e.g., a Darcy equation is contained in a Darcy-Stokes model or formulation or a related task

has characteristics: transitive

has super-properties
contained in op
has domain
Mathematical Formulation c
has range
Computational Task c or Mathematical Formulation c or Mathematical Model c
is inverse of
contains formulation op

contained as initial condition inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedAsInitialConditionIn

In mathematics and particularly in dynamic systems, an initial condition, in some contexts called a seed value,  is a value of an evolving variable at some point in time designated as the initial time (typically denoted t = 0)
has super-properties
contained in op
has domain
Mathematical Formulation c
has range
Computational Task c or Mathematical Formulation c or Mathematical Model c
is inverse of
contains initial condition op

contained as input inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedAsInputIn

Note that (base) quantities may be assigned as input or output or parameter in the context of a (specific!) mathematical task but not in the context of a (general!) model or equation.
has super-properties
contained in op
has domain
Quantity c or Quantity Kind c
has range
Computational Task c
is inverse of
contains input op

contained as objective inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedAsObjectiveIn

This property serves to indicate that a certain quantity is to be minimized or maximized in a mathematical optimization task.
has super-properties
contained in op
has domain
Quantity c or Quantity Kind c
has range
Computational Task c
is inverse of
contains objective op

contained as output inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedAsOutputIn

Note that (base) quantities may be assigned as input or output or parameter in the context of a (specific!) mathematical task but not in the context of a (general!) model or equation.
has super-properties
contained in op
has domain
Quantity c or Quantity Kind c
has range
Computational Task c
is inverse of
contains output op

contained as parameter inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedAsParameterIn

Note that (base) quantities may be assigned as input or output or parameter in the context of a (specific!) mathematical task but not in the context of a (general!) model or equation.
has super-properties
contained in op
has domain
Quantity c or Quantity Kind c
has range
Computational Task c
is inverse of
contains parameter op

contained in fieldop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedInField

A research problem is contained in a research field
has super-properties
contained in op
has domain
Research Problem c
has range
Research Field c
is inverse of
contains problem op

contained in formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedInFormulation

use this property to denote that a quantity is contained in a formulation e.g. masses are contained in a Newton Equation
has super-properties
contained in op
has domain
Quantity c or Quantity Kind c
has range
Mathematical Formulation c
is inverse of
contains quantity op

contained in modelop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedInModel

use this property to denote that a single model is included in a coupled model, e.g. a Darcy model and a Stokes model are included in a Darcy Stokes model

has characteristics: transitive

has super-properties
contained in op
has domain
Mathematical Model c
has range
Mathematical Model c
is inverse of
contains model op

contained in taskop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedInTask

This indicates that a computational sub-task is contained in a composite task.

has characteristics: transitive

has super-properties
contained in op
has domain
Computational Task c
has range
Computational Task c
is inverse of
contains task op

contains assumptionop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsAssumption

Assumptions in a mathematical model|task|formulation are the conditions that must be met for the mathematical model|task|formulation to be valid.
has super-properties
contains op
has domain
Computational Task c or Mathematical Formulation c or Mathematical Model c
has range
Mathematical Formulation c
is inverse of
contained as assumption in op

contains boundary conditionop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsBoundaryCondition

In the study of differential equations, a boundary-value problem is a differential equation subjected to constraints called boundary conditions.[1] A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions.
has super-properties
contains op
has domain
Computational Task c or Mathematical Formulation c or Mathematical Model c
has range
Mathematical Formulation c
is inverse of
contained as boundary condition in op

contains constantop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsConstant

This property serves to indicate that a certain quantity is considered as a constant in a computational task.
has super-properties
contains op
has domain
Computational Task c or Mathematical Formulation c
has range
Quantity c or Quantity Kind c
is inverse of
contained as constant in op

contains constraint conditionop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsConstraintCondition

Solutions to a computational task or a mathematical formulation or a mathematical model are subject to a constraint which is expressed as a mathematical formulation, i.e., an equation or an inequality
has super-properties
contains op
has domain
Computational Task c or Mathematical Formulation c or Mathematical Model c
has range
Mathematical Formulation c
is inverse of
contained as constraint condition in op

contains coupling conditionop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsCouplingCondition

Mathematical formulation, i.e., typically an equation, serving to model the interaction of two or more (sub-)systems that are interacting with each other
has super-properties
contains op
has domain
Computational Task c or Mathematical Formulation c or Mathematical Model c
has range
Mathematical Formulation c
is inverse of
contained as coupling condition in op

contains final conditionop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsFinalCondition

Similar to initial conditions. Sometimes used in the context of optimal control.
has super-properties
contains op
has domain
Computational Task c or Mathematical Formulation c or Mathematical Model c
has range
Mathematical Formulation c
is inverse of
contained as final condition in op

contains formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsFormulation

use this property to denote that a (single or coupled) model or formulation includes a mathematical formulation, e.g. a Darcy Stokes model includes a Darcy equation and a Stokes equation

has characteristics: transitive

has super-properties
contains op
has domain
Computational Task c or Mathematical Formulation c or Mathematical Model c
has range
Mathematical Formulation c
is inverse of
contained as formulation in op

contains initial conditionop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsInitialCondition

In mathematics and particularly in dynamic systems, an initial condition, in some contexts called a seed value,  is a value of an evolving variable at some point in time designated as the initial time (typically denoted t = 0).
has super-properties
contains op
has domain
Computational Task c or Mathematical Formulation c or Mathematical Model c
has range
Mathematical Formulation c
is inverse of
contained as initial condition in op

contains inputop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsInput

Indicates that a (base) quantity is considered as input in the context of a (specific!) computational task.
has super-properties
contains op
has domain
Computational Task c
has range
Quantity c or Quantity Kind c
is inverse of
contained as input in op

contains modelop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsModel

use this property to denote that a coupled model includes single models, e.g. a Darcy Stokes model includes a Darcy model and a Stokes model

has characteristics: transitive

has super-properties
contains op
has domain
Mathematical Model c
has range
Mathematical Model c
is inverse of
contained in model op

contains objectiveop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsObjective

This property serves to indicate that a certain quantity is to be minimized or maximized in a computational optimization task. An objective function, a target function, a loss function or cost function (minimization), a utility function or fitness function (maximization), or, in certain fields, an energy function or energy functional.
has super-properties
contains op
has domain
Computational Task c
has range
Quantity c or Quantity Kind c
is inverse of
contained as objective in op

contains outputop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsOutput

Indicates that a (base) quantity is considered as output in the context of a (specific!) computational task.
has super-properties
contains op
has domain
Computational Task c
has range
Quantity c or Quantity Kind c
is inverse of
contained as output in op

contains parameterop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsParameter

Auxiliary variable or arbitrary constant that characterizes a system or specifies a mathematical function among a family of functions. This property serves to indicate that a certain quantity is considered as a parameter in a computational task.
has super-properties
contains op
has domain
Computational Task c
has range
Quantity c or Quantity Kind c
is inverse of
contained as parameter in op

contains problemop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsProblem

A research field contains a research problem
has super-properties
contains op
has domain
Research Field c
has range
Research Problem c
is inverse of
contained in field op

contains quantityop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsQuantity

use this property to denote that a mathematical formulation contains a quantity, e.g., a Newton Equation contains masses
has super-properties
contains op
has domain
Mathematical Formulation c
has range
Quantity c or Quantity Kind c
is inverse of
contained in formulation op

contains taskop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsTask

This indicates that a composite computational task contains a subtask.

has characteristics: transitive

has super-properties
contains op
has domain
Computational Task c
has range
Computational Task c
is inverse of
contained in task op

defined byop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#definedBy

A quantity is defined by a mathematical formulation, i.e., an equation
has domain
Quantity c or Quantity Kind c
has range
Mathematical Formulation c
is inverse of
defines op

definesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#defines

A mathematical formulation, i.e., an equation, serves to define a quantity
has domain
Mathematical Formulation c
has range
Quantity c or Quantity Kind c
is inverse of
defined by op

discretized byop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#discretizedBy

Discrete models are the discrete analogues of continuous models. In discrete modelling, processes are described by discrete data, i.e., data that could potentially take on only a countable set of values, such as the integers, and which are not infinitely divisible. Thus, discrete modeling yields a computer representable and computable versions of continuous mathematical models,
has sub-properties
discretized by formulation op, discretized by model op, discretized by task op
is inverse of
discretizes op

discretized by formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#discretizedByFormulation

Discretizing is the process of obtaining discrete formulations that are the analogues of continuous formulations. Thus, discretization yields a computer representable and computable versions.
has super-properties
discretized by op
has domain
Mathematical Formulation c
has range
Mathematical Formulation c
is inverse of
discretizes formulation op

discretized by modelop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#discretizedByModel

Discretizing is the process of obtaining discrete models that are the analogues of continuous models. Thus, discretization yields a computer representable and computable versions. Note that certain models are already discretized from the outset.
has super-properties
discretized by op
has domain
Mathematical Model c
has range
Mathematical Model c
is inverse of
discretizes model op

discretized by taskop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#discretizedByTask

Discretizing is the process of obtaining discrete models that are the analogues of continuous models. Thus, discretization yields a computer representable and computable versions. Note that certain models are already discretized from the outset.
has super-properties
discretized by op
has domain
Computational Task c
has range
Computational Task c
is inverse of
discretizes task op

discretizesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#discretizes

Discretizing is the process of obtaining discrete models/formulations that are the analogues of continuous models/formulations. Thus, discretization yields a computer representable and computable versions.
has sub-properties
discretizes formulation op, discretizes model op, discretizes task op
is inverse of
discretized by op

discretizes formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#discretizesFormulation

Discretizing is the process of obtaining discrete formulations that are the analogues of continuous formulations. Thus, discretization yields a computer representable and computable versions.
has super-properties
discretizes op
has domain
Mathematical Formulation c
has range
Mathematical Formulation c
is inverse of
discretized by formulation op

discretizes modelop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#discretizesModel

Discretizing is the process of obtaining discrete models that are the analogues of continuous models, thus making them computer representable and hopefully(!) computer solvable. Note that certain models are already discretized from the outset.
has super-properties
discretizes op
has domain
Mathematical Model c
has range
Mathematical Model c
is inverse of
discretized by model op

discretizes taskop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#discretizesTask

has super-properties
discretizes op
has domain
Computational Task c
has range
Computational Task c
is inverse of
discretized by task op

documented inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#documentedIn

A property to express that an entity (problem, model, ...) is documented in a specific Publication
has domain
Computational Task c or Mathematical Formulation c or Mathematical Model c or Quantity c or Quantity Kind c or Research Field c or Research Problem c
has range
Publication c
is inverse of
documents op

documentsop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#documents

A property that expresses a Publication is documenting some entity (problem, model, ...)
has domain
Publication c
has range
Computational Task c or Mathematical Formulation c or Mathematical Model c or Quantity c or Quantity Kind c or Research Field c or Research Problem c
is inverse of
documented in op

generalized byop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizedBy

form of abstraction whereby common properties of specific instances are formulated as general concepts or claims

has characteristics: transitive

has sub-properties
generalized by field op, generalized by formulation op, generalized by model op, generalized by problem op, generalized by quantity op, generalized by task op
is inverse of
generalizes op

generalized by fieldop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizedByField

form of abstraction whereby common properties of specific instances are formulated as general concepts or claims

has characteristics: transitive

has super-properties
generalized by op
has domain
Research Field c
has range
Research Field c
is inverse of
generalizes field op

generalized by formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizedByFormulation

form of abstraction whereby common properties of specific instances are formulated as general concepts or claims

has characteristics: transitive

has super-properties
generalized by op
has domain
Mathematical Formulation c
has range
Mathematical Formulation c
is inverse of
generalizes formulation op

generalized by modelop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizedByModel

form of abstraction whereby common properties of specific instances are formulated as general concepts or claims

has characteristics: transitive

has super-properties
generalized by op
has domain
Mathematical Model c
has range
Mathematical Model c
is inverse of
generalizes model op

generalized by problemop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizedByProblem

form of abstraction whereby common properties of specific instances are formulated as general concepts or claims

has characteristics: transitive

has super-properties
generalized by op
has domain
Research Problem c
has range
Research Problem c
is inverse of
generalizes problem op

generalized by quantityop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizedByQuantity

form of abstraction whereby common properties of specific instances are formulated as general concepts or claims

has characteristics: transitive

has super-properties
generalized by op
has domain
Quantity c
has range
Quantity c or Quantity Kind c
is inverse of
generalizes quantity op

generalized by taskop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizedByTask

form of abstraction whereby common properties of specific instances are formulated as general concepts or claims

has characteristics: transitive

has super-properties
generalized by op
has domain
Computational Task c
has range
Computational Task c
is inverse of
generalizes task op

generalizesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizes

form of abstraction whereby common properties of specific instances are formulated as general concepts or claims

has characteristics: transitive

has sub-properties
generalizes field op, generalizes formulation op, generalizes model op, generalizes problem op, generalizes quantity op, generalizes task op
is inverse of
generalized by op

generalizes fieldop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizesField

form of abstraction whereby common properties of specific instances are formulated as general concepts or claims

has characteristics: transitive

has super-properties
generalizes op
has domain
Research Field c
has range
Research Field c
is inverse of
generalized by field op

generalizes formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizesFormulation

form of abstraction whereby common properties of specific instances are formulated as general concepts or claims

has characteristics: transitive

has super-properties
generalizes op
has domain
Mathematical Formulation c
has range
Mathematical Formulation c
is inverse of
generalized by formulation op

generalizes modelop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizesModel

form of abstraction whereby common properties of specific instances are formulated as general concepts or claims

has characteristics: transitive

has super-properties
generalizes op
has domain
Mathematical Model c
has range
Mathematical Model c
is inverse of
generalized by model op

generalizes problemop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizesProblem

form of abstraction whereby common properties of specific instances are formulated as general concepts or claims

has characteristics: transitive

has super-properties
generalizes op
has domain
Research Problem c
has range
Research Problem c
is inverse of
generalized by problem op

generalizes quantityop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizesQuantity

form of abstraction whereby common properties of specific instances are formulated as general concepts or claims

has characteristics: transitive

has super-properties
generalizes op
has domain
Quantity c or Quantity Kind c
has range
Quantity c
is inverse of
generalized by quantity op

generalizes taskop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizesTask

form of abstraction whereby common properties of specific instances are formulated as general concepts or claims

has characteristics: transitive

has super-properties
generalizes op
has domain
Computational Task c
has range
Computational Task c
is inverse of
generalized by task op

invented inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#inventedIn

A property that states that some entity (problem, model, ...) was invented in a specific Publication
has domain
Computational Task c or Mathematical Formulation c or Mathematical Model c or Quantity c or Quantity Kind c or Research Field c or Research Problem c
has range
Publication c
is inverse of
invents op

inventsop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#invents

A property that states that a Publication invented some entity (problem, model, ...)
has domain
Publication c
has range
Computational Task c or Mathematical Formulation c or Mathematical Model c or Quantity c or Quantity Kind c or Research Field c or Research Problem c
is inverse of
invented in op

linearized byop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#linearizedBy

A property that states that a formulation is linearized (exact or approximate) by another formulation.
has sub-properties
linearized by formulation op, linearized by model op, linearized by quantity op, linearized by task op
is inverse of
linearizes op

linearized by formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#linearizedByFormulation

A property that states that a formulation is linearized (exact or approximate) by another formulation.
has super-properties
linearized by op
has domain
Mathematical Formulation c
has range
Mathematical Formulation c
is inverse of
linearizes formulation op

linearized by modelop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#linearizedByModel

A property that states that a model is linearized (exact or approximate) by another model.
has super-properties
linearized by op
has domain
Mathematical Model c
has range
Mathematical Model c
is inverse of
linearizes model op

linearized by quantityop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#linearizedByQuantity

A property that states that a quantity is linearized (exact or approximate) by another quantity.
has super-properties
linearized by op
has domain
Quantity c
has range
Quantity c
is inverse of
linearizes quantity op

linearized by taskop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#linearizedByTask

A property that states that a task is linearized (exact or approximate) by another task.
has super-properties
linearized by op
has domain
Computational Task c
has range
Computational Task c
is inverse of
linearizes task op

linearizesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#linearizes

Linearization of a formulation, model, quantity or task.
has sub-properties
linearizes formulation op, linearizes model op, linearizes quantity op, linearizes task op
is inverse of
linearized by op

linearizes formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#linearizesFormulation

A property that states that a formulation linearizes (exact or approximate) another formulation.
has super-properties
linearizes op
has domain
Mathematical Formulation c
has range
Mathematical Formulation c
is inverse of
linearized by formulation op

linearizes modelop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#linearizesModel

A property that states that a model linearizes (exact or approximate) another model.
has super-properties
linearizes op
has domain
Mathematical Model c
has range
Mathematical Model c
is inverse of
linearized by model op

linearizes quantityop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#linearizesQuantity

A property that states that a quantity linearizes (exact or approximate) another quantity.
has super-properties
linearizes op
has domain
Quantity c
has range
Quantity c
is inverse of
linearized by quantity op

linearizes taskop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#linearizesTask

A property that states that a task linearizes (exact or approximate) another task.
has super-properties
linearizes op
has domain
Computational Task c
has range
Computational Task c
is inverse of
linearized by task op

modeled byop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#modeledBy

Mathematical modeling describes a part of the reality, the aim of which is to make a particular part or feature of the world easier to understand, define, quantify, visualize, or simulate by referencing it to existing and usually commonly accepted knowledge. It requires selecting and identifying relevant aspects of a situation in the real world and then developing a model to replicate a system with those features.
has domain
Research Problem c
has range
Mathematical Model c
is inverse of
models op

modelsop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#models

Mathematical modeling describes a part of the reality, the aim of which is to make a particular part or feature of the world easier to understand, define, quantify, visualize, or simulate by referencing it to existing and usually commonly accepted knowledge. It requires selecting and identifying relevant aspects of a situation in the real world and then developing a model to replicate a system with those features.
has domain
Mathematical Model c
has range
Research Problem c
is inverse of
modeled by op

nondimensionalized byop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#nondimensionalizedBy

Partial or full removal of physical dimensions from a quantity or a formulation

has characteristics: inverse functional

has sub-properties
nondimensionalized by formulation op, nondimensionalized by quantity op
is inverse of
nondimensionalizes op

nondimensionalized by formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#nondimensionalizedByFormulation

A property that states that a formulation is nondimensionalized (partially or completely) by another formulation.
has super-properties
nondimensionalized by op
has domain
Mathematical Formulation c
has range
Mathematical Formulation c
is inverse of
nondimensionalizes formulation op

nondimensionalized by quantityop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#nondimensionalizedByQuantity

A property that states that a quantity is nondimensionalized (partially or completely) by another quantity.
has super-properties
nondimensionalized by op
has domain
Quantity c or Quantity Kind c
has range
Quantity c or Quantity Kind c
is inverse of
nondimensionalizes quantity op

nondimensionalizesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#nondimensionalizes

Partial or full removal of physical dimensions from a quantity or a formulation

has characteristics: functional

has sub-properties
nondimensionalizes formulation op, nondimensionalizes quantity op
is inverse of
nondimensionalized by op

nondimensionalizes formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#nondimensionalizesFormulation

A property that states that a formulation nondimensionalizes (partially or completely) another formulation.
has super-properties
nondimensionalizes op
has domain
Mathematical Formulation c
has range
Mathematical Formulation c
is inverse of
nondimensionalized by formulation op

nondimensionalizes quantityop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#nondimensionaliesQuantity

A property that states that a quantity nondimensionalizes (partially or completely) another quantity.
has super-properties
nondimensionalizes op
has domain
Quantity c or Quantity Kind c
has range
Quantity c or Quantity Kind c
is inverse of
nondimensionalized by quantity op

similar toop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#similarTo

use this property only if the two things are similar but the one is not the generalization of the other one

has characteristics: symmetric, transitive

has sub-properties
similar to field op, similar to formulation op, similar to model op, similar to problem op, similar to quantity op, similar to task op

similar to fieldop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#similarToField

use this property only if the two research fields are similar but the one is not the generalization of the other one

has characteristics: symmetric, transitive

has super-properties
similar to op
has domain
Research Field c
has range
Research Field c

similar to formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#similarToFormulation

use this property only if the two mathematical formulations are similar but the one is not the generalization of the other one

has characteristics: symmetric, transitive

has super-properties
similar to op
has domain
Mathematical Formulation c
has range
Mathematical Formulation c

similar to modelop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#similarToModel

use this property only if the two mathematical models are similar but the one is not the generalization of the other one

has characteristics: symmetric, transitive

has super-properties
similar to op
has domain
Mathematical Model c
has range
Mathematical Model c

similar to problemop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#similarToProblem

use this property only if the two research problems are similar but the one is not the generalization of the other one

has characteristics: symmetric, transitive

has super-properties
similar to op
has domain
Research Problem c
has range
Research Problem c

similar to quantityop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#similarToQuantity

use this property only if the two quantities are similar but the one is not the generalization of the other one

has characteristics: symmetric, transitive

has super-properties
similar to op
has domain
Quantity c or Quantity Kind c
has range
Quantity c or Quantity Kind c

similar to taskop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#similarToTask

use this property only if the two computational tasks are similar but the one is not the generalization of the other one

has characteristics: symmetric, transitive

has super-properties
similar to op
has domain
Computational Task c
has range
Computational Task c

studied inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#studiedIn

This property states that an entity (problem, model, ...) is studied in a specific Publication
has domain
Computational Task c or Mathematical Formulation c or Mathematical Model c or Quantity c or Quantity Kind c or Research Field c or Research Problem c
has range
Publication c
is inverse of
studies op

studiesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#studies

This property states that a Publication studies an entity (problem, model, ...)
has domain
Publication c
has range
Computational Task c or Mathematical Formulation c or Mathematical Model c or Quantity c or Quantity Kind c or Research Field c or Research Problem c
is inverse of
studied in op

surveyed inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#surveyedIn

This property states that an entity (problem, model, application, ...) is surveyed in a specific Publication. Surveys are e.g. a review article, a handbook, an encyclopedia, monographs, a documentation, technical report ... .
has domain
Computational Task c or Mathematical Formulation c or Mathematical Model c or Quantity c or Quantity Kind c or Research Field c or Research Problem c
has range
Publication c
is inverse of
surveys op

surveysop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#surveys

This property states that a Publication surveys some entity (problem, model, application...). Surveys are e.g. a review article, a handbook, an encyclopedia, monographs, a documentation, technical report ... .
has domain
Publication c
has range
Computational Task c or Mathematical Formulation c or Mathematical Model c or Quantity c or Quantity Kind c or Research Field c or Research Problem c
is inverse of
surveyed in op

used inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#usedIn

A property that states that an entity (problem, model, ...) is used in a Publication
has domain
Computational Task c or Mathematical Formulation c or Mathematical Model c or Quantity c or Quantity Kind c or Research Field c or Research Problem c
has range
Publication c
is inverse of
uses op

usesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#uses

A property that states that a Publication uses a specific entity (problem, model, ...)
has domain
Publication c
has range
Computational Task c or Mathematical Formulation c or Mathematical Model c or Quantity c or Quantity Kind c or Research Field c or Research Problem c
is inverse of
used in op

Data Properties

defining formulationdp back to ToC or Data Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#definingFormulation

Equations, inequalities, expressions, logic quantifiers, ... in Latex or MathML, e.g. $F = ma$, $v \llt c$, $\forall n \in N$, ...
has super-properties
formulation property dp
has domain
Mathematical Formulation c
has range
La Te X ep or Math M L ep

formulation propertydp back to ToC or Data Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#formulationProperty

has sub-properties
defining formulation dp, in defining formulation dp
has domain
Mathematical Formulation c

in defining formulationdp back to ToC or Data Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#inDefiningFormulation

Symbol / Term of formulation and corresponding quantity in comma-separated list, e.g. ($\mathbf{F}$,qudt:Force) and/or ($m$,dbpedia:Mass) and/or ($\mathbf{a}$,wikidata:Q11376)
has super-properties
formulation property dp
has domain
Mathematical Formulation c
has range
string or La Te X ep or Math M L ep

is convexdp back to ToC or Data Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#isConvex

Boolean. True if convex, false if concave
has domain
Mathematical Formulation c or Mathematical Model c
has range
boolean

is deterministicdp back to ToC or Data Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#isDeterministic

Boolean. True, if the model is deterministic; false, if the model is probabilistic (stochastic)
has domain
Mathematical Formulation c or Mathematical Model c
has range
boolean

is dimensionlessdp back to ToC or Data Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#isDimensionless

has domain
Mathematical Formulation c or Mathematical Model c or Quantity c or Quantity Kind c
has range
boolean

is dynamicdp back to ToC or Data Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#isDynamic

Boolean. True, if dynamic; false, if static
has domain
Mathematical Formulation c or Mathematical Model c
has range
boolean

is lineardp back to ToC or Data Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#isLinear

Boolean. True, if linear; false, if non-linear
has domain
Computational Task c or Mathematical Formulation c or Mathematical Model c or Quantity c
has range
boolean

is space-continuousdp back to ToC or Data Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#isSpaceContinuous

Boolean. True, if continuous in space; false, if discrete in space
has domain
Mathematical Formulation c or Mathematical Model c
has range
boolean

is time-continuousdp back to ToC or Data Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#isTimeContinuous

Boolean. True, if continuous in time; false, if discrete in time
has domain
Mathematical Formulation c or Mathematical Model c
has range
boolean

Annotation Properties

abstractap back to ToC or Annotation Property ToC

IRI: http://purl.org/dc/terms/abstract

alt Labelap back to ToC or Annotation Property ToC

IRI: http://www.w3.org/2004/02/skos/core#altLabel

arxiv I Dap back to ToC or Annotation Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#arxivID

bibliographic Citationap back to ToC or Annotation Property ToC

IRI: http://purl.org/dc/terms/bibliographicCitation

broaderap back to ToC or Annotation Property ToC

IRI: http://www.w3.org/2004/02/skos/core#broader

close Matchap back to ToC or Annotation Property ToC

IRI: http://www.w3.org/2004/02/skos/core#closeMatch

contributorap back to ToC or Annotation Property ToC

IRI: http://purl.org/dc/terms/contributor

createdap back to ToC or Annotation Property ToC

IRI: http://purl.org/dc/terms/created

creatorap back to ToC or Annotation Property ToC

IRI: http://purl.org/dc/terms/creator

dbpedia I Dap back to ToC or Annotation Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#dbpediaID

definitionap back to ToC or Annotation Property ToC

IRI: http://www.w3.org/2000/01/rdf-schema#definition

descriptionap back to ToC or Annotation Property ToC

IRI: http://purl.org/dc/terms/description

doi I Dap back to ToC or Annotation Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#doiID

is Replaced Byap back to ToC or Annotation Property ToC

IRI: http://purl.org/dc/terms/isReplacedBy

issuedap back to ToC or Annotation Property ToC

IRI: http://purl.org/dc/terms/issued

licenseap back to ToC or Annotation Property ToC

IRI: http://purl.org/dc/terms/license

mardi I Dap back to ToC or Annotation Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#mardiID

modifiedap back to ToC or Annotation Property ToC

IRI: http://purl.org/dc/terms/modified

publisherap back to ToC or Annotation Property ToC

IRI: http://purl.org/dc/terms/publisher

qudt I Dap back to ToC or Annotation Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#qudtID

referencesap back to ToC or Annotation Property ToC

IRI: http://purl.org/dc/terms/references

rightsap back to ToC or Annotation Property ToC

IRI: http://purl.org/dc/terms/rights

subjectap back to ToC or Annotation Property ToC

IRI: http://purl.org/dc/terms/subject

titleap back to ToC or Annotation Property ToC

IRI: http://purl.org/dc/terms/title

was Derived Fromap back to ToC or Annotation Property ToC

IRI: http://www.w3.org/ns/prov#wasDerivedFrom

wikidata I Dap back to ToC or Annotation Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#wikidataID

zbmath I Dap back to ToC or Annotation Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#zbmathID

Named Individuals

Accelerationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Acceleration

Rate at which the magnitude and/or direction of velocity changes with time
belongs to
Quantity Kind c
has facts
qudt I D ap Acceleration ep
wikidata I D ap Q11376 ep

Action Potential Propagation Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Action_Potential_Propagation_Model

Accounts for the propagation of the action potential. Necessary because Subcellular model only considers isolated processes in one sacomere
belongs to
Mathematical Model c
has facts
studied in op Homs-Pons (2024) Coupled simulations and parameter inversion for neural system and electrophysiological muscle models ni
is deterministic dp "true"^^boolean
is dynamic dp "true"^^boolean
is space-continuous dp "true"^^boolean
is time-continuous dp "true"^^boolean
description ap "propagation of the action potential"@en
doi I D ap gamm.202370009 ep

Active Contractile Forceni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ActiveContractileForce

belongs to
Quantity c
has facts
defined by op Active Contractile Force (Definition) ni
description ap "active force generated by the contractile element"@en

Active Contractile Force (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ActiveContractileForceDefinition

belongs to
Mathematical Formulation c
has facts
contains quantity op Active Contractile Force ni
contains quantity op Maximum Isometric Muscle Force ni
contains quantity op Muscle Contraction Velocity ni
contains quantity op Muscle Length ni
contains quantity op Time ni
defining formulation dp "$F_{\text{ACE}}(t) \equiv F^{\text{M}}_{0} \cdot a(t) \cdot f_{\text{L}}(\mathcal{l}_{\text{M}}(t)) \cdot f_{\text{v}} (\nu_{\text{M}}(t))$"^^La Te X ep
in defining formulation dp "$F^{\text{M}}_{0}$, Maximum Isometric Muscle Force"^^La Te X ep
in defining formulation dp "$F_{\text{ACE}}$, Active Contractile Force"^^La Te X ep
in defining formulation dp "$\mathcal{l}_{\text{M}}$, Muscle Length"^^La Te X ep
in defining formulation dp "$\nu_{\text{M}}$, Muscle Contraction Velocity"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
description ap "active force generated by the contractile element"@en

Age Of An Individualni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AgeOfAnIndividual

belongs to
Quantity c
has facts
generalized by quantity op Time ni
is dimensionless dp "true"^^boolean
description ap "time elapsed since an individual was born"@en
wikidata I D ap Q185836 ep

Allee Effectni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AlleeEffect

The Allee effect is used to model the infection rate as a function of population density, where it represents a lower transmission probability in less densely populated regions. we adopt the effect and bound it from below by 1/3. This ensuresthat the effect is at most three times lower in sparsely populated areas than in regions with high population density. To enforce the lower bound, we apply a shift n0 in the Allee term. WE choose $n_0 = \frac{3}{2}A$
belongs to
Mathematical Formulation c
has facts
contained as boundary condition in op PDE SEIR Model ni
contains quantity op Allee Threshold ni
contains quantity op Population Density ni
defining formulation dp "$1 - \dfrac{A}{n + n_0} \geq \frac{1}{3}$"^^La Te X ep
in defining formulation dp "$A$, Allee Threshold"^^La Te X ep
in defining formulation dp "$n$, Population Density"^^La Te X ep
wikidata I D ap Q2301505 ep

Allee Thresholdni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AlleeThreshold

belongs to
Quantity c
has facts
description ap "population density below which growth becomes negative"@en

Ampere Lawni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AmpereLaw

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Maxwell Equations Model ni
contains quantity op Electric Current Density ni
contains quantity op Electric Field ni
contains quantity op Magnetic Field ni
contains quantity op Permeability (Vacuum) ni
contains quantity op Permittivity (Vacuum) ni
contains quantity op Time ni
defining formulation dp "$\nabla \times \mathbf{B} &= \mu_0\left(\mathbf{J} + \epsilon_0 \frac{\partial \mathbf{E}} {\partial t} \right$"^^La Te X ep
in defining formulation dp "$E$, Electric Field"^^La Te X ep
in defining formulation dp "$E$, Magnetic Field"^^La Te X ep
in defining formulation dp "$J$, Electric Current Density"^^La Te X ep
in defining formulation dp "$\epsilon_0$, Permittivity (Vacuum)"^^La Te X ep
in defining formulation dp "$\mu_0$, Permeability (Vacuum)"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
description ap "Ampère's circuital law (with Maxwell's addition) relates the integrated magnetic field around a closed loop to the electric current passing through the loop"@en
wikidata I D ap Q51500 ep

Amplitude Of Electron Waveni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AmplitudeOfElectronWave

belongs to
Quantity c
has facts
contained in formulation op Darwin-Howie-Whelan Equation for an unstrained crystal ni
contained in formulation op Darwin-Howie-Whelan Equation for a strained crystal ni
contained in formulation op Initial Value For Electron Scattering ni
description ap "amplitude of the wave function representing an electron"@en

Angular Momentumni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AngularMomentum

measure of the extent to which an object will continue to rotate in the absence of an applied torque
belongs to
Quantity Kind c
has facts
generalizes quantity op Planck Constant ni
qudt I D ap Angular Momentum ep
wikidata I D ap Q161254 ep

Anharmonicity Constantni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AnharmonicityConstant

belongs to
Quantity c
has facts
defined by op Anharmonicity Constant (Definition) ni
description ap "deviation of a physical system from being a harmonic oscillator"@en
wikidata I D ap Q545228 ep

Anharmonicity Constant (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AnharmonicityConstantDefinition

Derived by using second order (non-degenerate) perturbation theory, considering the comparable magnitude of contributions of cubic anharmonicity in second order and quartic anharmonicity in first order.
belongs to
Mathematical Formulation c
has facts
contains quantity op Anharmonicity Constant ni
contains quantity op Coriolis Coupling Constant ni
contains quantity op Force Constant (Anharmonic) ni
contains quantity op Number of Particles ni
contains quantity op Rotational Constant ni
contains quantity op Vibration Frequency (Harmonic) ni
defining formulation dp "$ \begin{align} \chi_{rr} &=& \frac{1}{16} \phi_{rrrr} - \frac{1}{16} \sum_{s=1}^{3N-6} \phi_{rrs}^2 \frac {8\omega_r^2-3\omega_s^2} {\omega_s(4\omega_r^2-\omega_s^2)} \\ \chi_{rs} &=&\frac{1}{4} \phi_{rrss} - \frac{1}{4} \sum_{t=1}^{3N-6} \frac{\phi_{rrt}\phi_{tss}}{\omega_t} - \frac{1}{2} \sum_{t=1}^{3N-6} \frac {\phi_{rst}^2 \omega_t (\omega_t^2-\omega_r^2-\omega_s^2)} {\Delta_{rst}} \\ &+& \left[ A(\zeta_{r,s}^{(a)})^2 + B(\zeta_{r,s}^{(b)})^2 + C(\zeta_{r,s}^{(c)})^2 \right] \left[ \frac{\omega_r}{\omega_s} + \frac{\omega_s}{\omega_r} \right] \\ \Delta_{rst} &=& ( \omega_r + \omega_s + \omega_t ) ( \omega_r - \omega_s - \omega_t ) (-\omega_r + \omega_s - \omega_t ) (-\omega_r - \omega_s + \omega_t ) \end{align}$"^^La Te X ep
in defining formulation dp "$A,B,C$, Rotational Constant"^^La Te X ep
in defining formulation dp "$N$, Number of Particles"^^La Te X ep
in defining formulation dp "$\chi$, Anharmonicity Constant"^^La Te X ep
in defining formulation dp "$\omega$, Vibrational Frequency (Harmonic)"^^La Te X ep
in defining formulation dp "$\phi$, Force Constant (Anharmonic)"^^La Te X ep
in defining formulation dp "$\zeta$, Coriolis Coupling Constant"^^La Te X ep
wikidata I D ap Q545228 ep

Applied External Voltageni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AppliedExternalVoltage

belongs to
Quantity c
has facts
contained in formulation op Dirichlet Boundary Condition For Electric Potential ni
generalized by quantity op Voltage ni
description ap "external voltage at an Ohmic contact in semiconductor physics|technology"@en

Archaeologyni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Archaeology

belongs to
Research Field c
has facts
generalizes field op Egyptology ni
description ap "study of the past via material culture"@en
mardi I D ap Item: Q65133 ep
wikidata I D ap Q23498 ep

Areani back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Area

Quantity that expresses the extent of a two-dimensional surface or shape, or planar lamina, in the plane
belongs to
Quantity Kind c
has facts
wikidata I D ap Q11500 ep

Artificial Neural Networkni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Artificial_Neural_Network

belongs to
Mathematical Model c
has facts
wikidata I D ap Q192776 ep

Astronomyni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Astronomy

belongs to
Research Field c
has facts
description ap "scientific study of celestial objects and phenomena"@en
mardi I D ap Item: Q71225 ep
wikidata I D ap Q333 ep

Asymptomatic Infection Rateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AsymptomaticInfectionRate

belongs to
Quantity c
has facts
generalized by quantity op Rate ni
description ap "constant representing the asymptomatic infection rate"@en

Asymptomatic Recovery Rateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AsymptomaticRecoveryRate

belongs to
Quantity c
has facts
generalized by quantity op Rate ni
description ap "constant representing the asymptomatic recovery rate"@en

Attraction Force At Opinionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AttractionForceAtOpinion

belongs to
Quantity c

Attraction Force At Opinion Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AttractionForceAtOpinionFormulation

Attraction Force at a specific opinion x
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Partial Mean Field Opinion Model ni
contains quantity op Attraction Force At Opinion ni
contains quantity op Opinion ni
contains quantity op Overall Distribution Of Individuals ni
contains quantity op Pair Function ni
contains quantity op Parameter To Scale Attractive Force From Influencers ni
contains quantity op Parameter To Scale Attractive Force From Media ni
contains quantity op Parameter To Scale Attractive Force From Other Individuals ni
defining formulation dp "$\mathcal{F}(x, y_m, z_l, \rho) = a \frac{\int_D \rho(x', t) \varphi(\|x' - x\|)(x' - x) \, dx'}{\int_D \rho(x', t) \varphi(\|x' - x\|) \, dx'} + b (y_m(t) - x) + c (z_l(t) - x)$"^^La Te X ep
in defining formulation dp "$\mathcal{F}$, Attraction Force At Opinion"^^La Te X ep
in defining formulation dp "$\phi$, Pair Function"^^La Te X ep
in defining formulation dp "$\rho$, Overall Distribution Of Individuals"^^La Te X ep
in defining formulation dp "$a$, Parameter To Scale Attractive Force From Other Individuals"^^La Te X ep
in defining formulation dp "$b$, Parameter To Scale Attractive Force From Media"^^La Te X ep
in defining formulation dp "$c$, Parameter To Scale Attractive Force From Influencers"^^La Te X ep
in defining formulation dp "$x$, Opinion"^^La Te X ep

Average Opinion Of Followers Of Influencersni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AverageOpinionOfInfluencerFollowers

belongs to
Quantity c
has facts
description ap "opinion of the influencers is drawn towards the average opinion of the followers"@en

Average Opinion Of Followers Of Influencers In The Partial Mean Field Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AverageOpinionOfFollowersOfInfluencersInThePartialFieldModel

belongs to
Quantity c
has facts
description ap "opinion of the influencers is drawn towards the average opinion of the followers"@en

Average Opinion Of Followers Of Infuencers Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AverageOpinionOfFollowersOfInfluencersFormulation

Equation describing the average opinon of the followers of a specific Influencer. The influencer's opinion will also be attracted towards this average opinion
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Opinion Model With Influencers And Media ni
contains quantity op Average Opinion Of Followers Of Influencers ni
contains quantity op Influencer Individual Matrix ni
contains quantity op Opinion Vector of Individuals ni
contains quantity op Time ni
defining formulation dp "$\hat{x}_l(t)=\frac{1}{\sum_k C_{k l}(t)} \sum_{i=1}^N C_{i l}(t) x_i(t)$"^^La Te X ep
in defining formulation dp "$C_l(t)$, Influencer Individual Matrix"^^La Te X ep
in defining formulation dp "$\hat{x}_l(t)$, Average Opinion Of Followers Of Influencers"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$x_i(t)$, Opinion Vector of Individuals"^^La Te X ep
is space-continuous dp "true"^^boolean

Average Opinion Of Followers Of Infuencers In The Partial Mean Field Model Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AverageOpinionOfFollowersOfInfluencersInThePartialFieldModelFormulation

Equation describing the average opinon of the followers of a specific Influencer in the partial field opinion model. The influencer's opinion will also be attracted towards this average opinion
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Partial Mean Field Opinion Model ni
contains quantity op Average Opinion Of Followers Of Influencers In The Partial Mean Field Model ni
contains quantity op Limiting Distribution Of Individuals ni
contains quantity op Medium Influencer Fraction Limit ni
contains quantity op Opinion ni
contains quantity op Time ni
defining formulation dp "$\hat{x}_l(t)=\frac{\sum_{m=1}^M \int_D x \rho_{m, l}(x, t) d x}{\sum_{m=1}^M n_{m, l}(t)}$"^^La Te X ep
in defining formulation dp "$\hat{x}_l(t)$, Average Opinion Of Followers Of Infuencers In The Partial Field Model"^^La Te X ep
in defining formulation dp "$\rho_{m,l}$, Limiting Distribution Of Individuals"^^La Te X ep
in defining formulation dp "$n_{m,l}$, Medium Influencer Fraction Limit"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$x$, Opinion"^^La Te X ep

Average Opinion Of Followers Of Mediani back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AverageOpinionOfMediaFollowers

belongs to
Quantity c
has facts
description ap "opinion of the media is drawn towards the average opinion of the followers of that medium"@en

Average Opinion Of Followers Of Media Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AverageOpinionOfFollowersOfMediaFormulation

Equation describing the average opinon of the followers of a specific Medium. The Medium's opinion will also be attracted towards this average opinion.
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Opinion Model With Influencers And Media ni
contains quantity op Average Opinion Of Followers Of Media ni
contains quantity op Medium Follower Matrix ni
contains quantity op Opinion Vector of Individuals ni
contains quantity op Time ni
defining formulation dp "$\tilde{x}_m(t)=\frac{1}{\sum_k B_{k m}(t)} \sum_{i=1}^N B_{i m}(t) x_i(t) $"^^La Te X ep
in defining formulation dp "$B_m(t)$, Medium Follower Matrix"^^La Te X ep
in defining formulation dp "$\tilde{x}_m(t)$, Average Opinion Of Followers Of Media"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$x_i(t)$, Opinion Vector of Individuals"^^La Te X ep
is deterministic dp "false"^^boolean
is dimensionless dp "false"^^boolean
is space-continuous dp "true"^^boolean

Average Opinion Of Followers Of Media In The Partial Mean Field Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AverageOpinionOfFollowersOfMediaInThePartialFieldModel

belongs to
Quantity c
has facts
description ap "opinion of the media is drawn towards the average opinion of the followers of that medium"@en

Average Opinion Of Followers Of Media In The Partial Mean Field Model Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AverageOpinionOfFollowersOfMediaInThePartialFieldModelFormulation

Equation describing the average opinon of the followers of a specific Medium in the partial field opinion model. The Medium's opinion will also be attracted towards this average opinion
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Partial Mean Field Opinion Model ni
contains quantity op Average Opinion Of Followers Of Media In The Partial Mean Field Model ni
contains quantity op Limiting Distribution Of Individuals ni
contains quantity op Medium Influencer Fraction Limit ni
contains quantity op Opinion ni
contains quantity op Time ni
defining formulation dp "$\tilde{x}_m(t)=\frac{\sum_{l=1}^L \int_D x \rho_{m, l}(x, t) d x}{\sum_{l=1}^L n_{m, l}(t)}$"^^La Te X ep
in defining formulation dp "$\rho_{m,l}$, Limiting Distribution Of Individuals"^^La Te X ep
in defining formulation dp "$\tilde{x}_m(t)$, Average Opinion Of Followers Of Media In The Partial Field Model"^^La Te X ep
in defining formulation dp "$n_{m,l}$, Medium Influencer Fraction Limit"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$x$, Opinion"^^La Te X ep

Azimuthal Angleni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#AzimuthalAngle

Angle in the spherical coordinate system in the range $-\pi < \phi \leq \pi$
belongs to
Quantity Kind c
has facts
wikidata I D ap Q116757767 ep

Balanced Truncationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BalancedTruncation

The basic principle is to identify a subspace of jointly easily controllable and observable states and then to restrict the dynamics to this subspace, hopefully without changing the overall response of the system too much.
belongs to
Computational Task c
has facts
applies model op Control System Model ni
contains formulation op Balancing Transformation ni
contains formulation op Lyapunov Equation ni
generalizes task op Balanced Truncation (Linear) ni
description ap "powerful technique to reduce the state-space dimension of a dynamical system"@en
doi I D ap 3 540 27909 1 3 ep
doi I D ap 1.3605243 ep
doi I D ap jcd.2020001 ep

Balanced Truncation (Linear)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BalancedTruncationLinear

In the case of a linear control system, a useful property of balanced truncation is that it admits easy control of the approximation error when truncating states.
belongs to
Computational Task c
has facts
applies model op Control System Model (Linear) ni
contains formulation op Balancing Transformation ni
contains formulation op Control System Input Linear ni
contains formulation op Control System Input Linear (Reduced) ni
contains formulation op Control System Output Linear ni
contains formulation op Control System Output Linear (Reduced) ni
contains formulation op Lyapunov Equation Controllability ni
contains formulation op Lyapunov Equation Observability ni
contains initial condition op Initial Control State ni
contains input op Control System Matrix A ni
contains input op Control System Matrix B ni
contains input op Control System Matrix C ni
contains output op Control System Matrix A (Reduced) ni
contains output op Control System Matrix B (Reduced) ni
contains output op Control System Matrix C (Reduced) ni
contains output op MOR Transformation Matrix ni
description ap "powerful technique to reduce the state-space dimension of a dynamical system with linear input equation"@en

Balancing Transformationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BalancingTransformation

The transformation T is a contragredient transformation and exists whenever $W_c$, $W_o$ are symmetric and positive definite. Note that the squared HSVs are the eigenvalues of the product of $W_c$ and $W_o$.
belongs to
Mathematical Formulation c
has facts
contains quantity op Gramian Matrix Controllability ni
contains quantity op Gramian Matrix Observability ni
contains quantity op Hankel Singular Value ni
contains quantity op MOR Transformation Matrix ni
defining formulation dp "$T^{-1}W_c\left(T^{-1}\right)^{*} = T^{*}W_oT = \left( \begin{array}{lll} \sigma_{1} & & 0 \\ & \ddots & \\ 0 & & \sigma_{n} \end{array}\right) = \Sigma$"^^La Te X ep
in defining formulation dp "$T$, MOR Transformation Matrix"^^La Te X ep
in defining formulation dp "$W_c$, Gramian Matrix Controllability"^^La Te X ep
in defining formulation dp "$W_o$, Gramian Matrix Observability"^^La Te X ep
in defining formulation dp "$\sigma$, Hankel Singular Value"^^La Te X ep
description ap "coordinate transformation T under which controllability and observability Gramians become equal and diagonal matrices comprising the Hankel singular values"@en

Band Edge Energy For Conduction Bandni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BandEdgeEnergyForConductionBand

belongs to
Quantity c
has facts
generalized by quantity op Energy ni
description ap "energy of the lower edge of the electronic conduction band"@en

Band Edge Energy For Valence Bandni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BandEdgeEnergyForValenceBand

belongs to
Quantity c
has facts
generalized by quantity op Energy ni
description ap "energy of the upper edge of the electronic valence band"@en

Beavers-Joseph Coefficientni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BeaversJosephCoefficient

belongs to
Quantity c
has facts
description ap "coefficient for the coupling of a Stokes model and a Darcy model"@en

Beavers–Joseph-Saffman Conditionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BeaversJosephSaffmanCondition

belongs to
Mathematical Formulation c
has facts
contains quantity op Beavers-Joseph Coefficient ni
contains quantity op Fluid Dynamic Viscosity (Free Flow) ni
contains quantity op Fluid Intrinsic Permeability (Porous Medium) ni
contains quantity op Fluid Velocity (Free Flow) ni
contains quantity op Fluid Viscous Stress ni
contains quantity op Unit Normal Vector ni
contains quantity op Unit Tangent Vector ni
defining formulation dp "$[(v + \sqrt{K}(\alpha_{\mathrm{BJ}}\mu)^{-1} \tau n)\cdot t_{\mathrm{ff,pm}}]^{ff} = 0 \quad \mathrm {on} \quad \Gamma$"^^La Te X ep
in defining formulation dp "$K$, Fluid Intrinsic Permeability (Porous Medium)"^^La Te X ep
in defining formulation dp "$\alpha_{BJ}$, Beavers-Joseph Coefficient"^^La Te X ep
in defining formulation dp "$\mu$, Fluid Dynamic Viscosity (Free Flow)"^^La Te X ep
in defining formulation dp "$\tau$, Fluid Viscous Stress"^^La Te X ep
in defining formulation dp "$n$, Normal Unit Vector"^^La Te X ep
in defining formulation dp "$t_{\mathrm{ff,pm}}$, Tangent Unit Vector"^^La Te X ep
in defining formulation dp "$v^{ff}$, Fluid Velocity (Free Flow)"^^La Te X ep
description ap "boundary condition between an unconfined incompressible viscous fluid (Stokes model) and fluid inside a porous medium (Darcy model)"@en
doi I D ap s11242 009 9344 y ep
doi I D ap S0022112067001375 ep

Between Population Contact Rateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BetweenPopulationContactRate

Used in multi-population models.
belongs to
Quantity c
has facts
generalized by op Rate ni
is dimensionless dp "false"^^boolean
description ap "contact rate of one sub-population with all other sub-populations"@en

Between Population Contact Rate Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BetweenPopulationContactRateEquation

belongs to
Mathematical Formulation c
has facts
contains quantity op Between Population Contact Rate ni
contains quantity op Contact Rate ni
contains quantity op Time Step ni
contains quantity op Total Population Size ni
defines op Between Population Contact Rate ni
defining formulation dp "$a_i = \sum_{k\neq i}\alpha_{ik} \Delta t N^k/N^i$"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\N^i$, Total Population Size"^^La Te X ep
in defining formulation dp "$\alpha_{ik}$, Contact Rate"^^La Te X ep
in defining formulation dp "$a_i$, Between Population Contact Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean
description ap "contact rate of one sub-population(represented by subscript i) with all other subpopulations"@en

Bi Bi Reaction following Ordered Mechanismni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionfollowingOrderedMechanism

Bi Bi reaction with a sequential mechanism in which the substrates bind to the enzyme, are converted to products and released. Binding of substrates and unbinding of products occurs in an ordered sequence.
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni
generalized by problem op Bi Bi Reaction ni
generalizes problem op Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Product 1 ni
generalizes problem op Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Product 2 ni
generalizes problem op Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Products 1 and 2 ni
generalizes problem op Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism without Products ni

Bi Bi Reaction following Ordered Mechanism with single central complexni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionfollowingOrderedMechanismSingleCC

Bi Bi reaction with a sequential mechanism in which the substrates bind to the enzyme, are converted to products and released. Binding of substrates and unbinding of products occurs in an ordered sequence. A single central Complex is assumed.
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni
generalized by problem op Bi Bi Reaction ni
generalized by problem op Bi Bi Reaction following Ordered Mechanism ni
generalizes problem op Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Product 1 and single central Complex ni
generalizes problem op Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Product 2 and single central Complex ni
generalizes problem op Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Products 1 and 2 and single central Complex ni
generalizes problem op Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism without Products and single central Complex ni

Bi Bi Reaction following Ping Pong Mechanismni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionfollowingPingPongMechanism

Bi Bi reaction with a nonsequential mechanism in which the first product is formed and released before the second substrate binds. Binding of the first substrate transforms the enzyme into an intermediate state which must be resolved following the formation and release of the second product.
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni
generalizes problem op Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism with Product 1 ni
generalizes problem op Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism with Product 2 ni
generalizes problem op Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism with Products 1 and 2 ni
generalizes problem op Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism without Products ni

Bi Bi Reaction following Theorell-Chance Mechanismni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionfollowingTheorellChanceMechanism

Bi Bi reaction with a sequential mechanism in which the substrates bind to the enzyme, are converted to products and released. Binding of substrates and unbinding of products occurs in an ordered sequence, not triple complexes are formed.
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni

Bi Bi Reaction Ordered Mechanism (ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionOrderedMechanismODEModel

Ordinary differential equations for the rates of change of all chemical species (substrate 1 and 2, enzyme, enzyme - substrate 1 - complex, enzyme - substrate 1 - substrate 2 - complex, enzyme - product 1 - product 2 - complex, enzyme - product 1 complex and product 1 and 2 in a Bi Bi Reaction following the Ordered Mechanism. k_{i} with positive or negative i represents the rate constant of the forward- or backward-reaction i-th reaction step.
belongs to
Mathematical Model c
has facts
applied by task op Parameter Estimation of Enzyme Kinetics ni
applied by task op Sensitivity Analysis of Complex Kinetic Systems ni
applied by task op Simulation of Complex Kinetic Systems ni
contains formulation op Bi Bi Reaction Ordered Mechanism ODE System ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Enzyme Concentration (Bi Bi Reaction Ordered - ODE Model) ni
contains initial condition op Initial Enzyme - Product 1 - Complex Concentration (Bi Bi Reaction Ordered - ODE Model) ni
contains initial condition op Initial Enzyme - Product 1 - Product 2 - Complex Concentration (Bi Bi Reaction Ordered - ODE Model) ni
contains initial condition op Initial Enzyme - Substrate 1 - Complex Concentration (Bi Bi Reaction Ordered - ODE Model) ni
contains initial condition op Initial Enzyme - Substrate 1 - Substrate 2 - Complex Concentration (Bi Bi Reaction Ordered - ODE Model) ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Ordered - ODE Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Ordered - ODE Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Ordered - ODE Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Ordered - ODE Model) ni
models op Bi Bi Reaction following Ordered Mechanism ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "true"^^boolean
is linear dp "false"^^boolean
is time-continuous dp "true"^^boolean
description ap "bi bi reaction model following an ordered mechanism"@en

Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Product 1 (Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionOrderedMechanismMichaelisMentenModelwithProduct1SS

belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Ordered with Product 1 - Michaelis Menten Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Ordered without Product 2 - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
generalized by model op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Products 1 and 2 (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ordered Mechanism (ODE Model) ni
generalizes model op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Product 1 and single central Complex (Steady State Assumption) ni
models op Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Product 1 ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean
description ap "bi bi reaction Michaelis Menten model following an ordered mechanism with product 1 formulated via the steady state assumption"@en

Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Product 1 and single central Complex (Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionOrderedMechanismMichaelisMentenModelwithProduct1ansSingleCCSS

belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Ordered with Product 1 - Michaelis Menten Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Ordered without Product 2 - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
generalized by model op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Products 1 and 2 and single central Complex (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ordered Mechanism (ODE Model) ni
models op Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Product 1 and single central Complex ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean
description ap "bi bi reaction with single central complex Michaelis Menten model following an ordered mechanism with product 1 formulated via the steady state assumption"@en

Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Product 2 (Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionOrderedMechanismMichaelisMentenModelwithProduct2SS

belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Ordered without Product 1 - Michaelis Menten Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Ordered with Product 2 - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
generalized by model op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Products 1 and 2 (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ordered Mechanism (ODE Model) ni
generalizes model op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Product 2 and single central Complex (Steady State Assumption) ni
models op Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Product 2 ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean
description ap "bi bi reaction Michaelis Menten model following an ordered mechanism with product 2 formulated via the steady state assumption"@en

Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Product 2 and single central Complex (Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionOrderedMechanismMichaelisMentenModelwithProduct2ansSingleCCSS

belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Ordered without Product 1 - Michaelis Menten Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Ordered with Product 2 - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
generalized by model op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Products 1 and 2 and single central Complex (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ordered Mechanism (ODE Model) ni
models op Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Product 2 and single central Complex ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean
description ap "bi bi reaction with single central complex Michaelis Menten model following an ordered mechanism with product 2 formulated via the steady state assumption"@en

Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Products 1 and 2 (Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionOrderedMechanismMichaelisMentenModelwithProducts1and2SS

belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Ordered with Product 1 - Michaelis Menten Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Ordered with Product 2 - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
generalized by model op Bi Bi Reaction Ordered Mechanism (ODE Model) ni
generalizes model op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Products 1 and 2 and single central Complex (Steady State Assumption) ni
models op Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Products 1 and 2 ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean
description ap "bi bi reaction Michaelis Menten model following an ordered mechanism with products 1 and 2 formulated via the steady state assumption"@en

Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Products 1 and 2 and single central Complex (Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionOrderedMechanismMichaelisMentenModelwithProducts1and2ansSingleCCSS

belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Ordered with Product 1 - Michaelis Menten Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Ordered with Product 2 - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
generalized by model op Bi Bi Reaction Ordered Mechanism (ODE Model) ni
models op Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Products 1 and 2 and single central Complex ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean
description ap "bi bi reaction with single central complex Michaelis Menten model following an ordered mechanism with products 1 and 2 formulated via the steady state assumption"@en

Bi Bi Reaction Ordered Mechanism Michaelis Menten Model without Products (Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionOrderedMechanismMichaelisMentenModelwithoutProductsSS

belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Ordered without Product 1 - Michaelis Menten Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Ordered without Product 2 - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
generalized by model op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Product 1 (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Product 2 (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Products 1 and 2 (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ordered Mechanism (ODE Model) ni
generalizes model op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model without Products and single central Complex (Steady State Assumption) ni
models op Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism without Products ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean
description ap "bi bi reaction Michaelis Menten model following an ordered mechanism without products formulated via the steady state assumption"@en

Bi Bi Reaction Ordered Mechanism Michaelis Menten Model without Products and single central Complex (Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionOrderedMechanismMichaelisMentenModelwithoutProductsansSingleCCSS

belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Ordered without Product 1 - Michaelis Menten Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Ordered without Product 2 - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
generalized by model op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Product 1 and single central Complex (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Product 2 and single central Complex (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Products 1 and 2 and single central Complex (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ordered Mechanism (ODE Model) ni
models op Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism without Products and single central Complex ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean
description ap "bi bi reaction with single central complex Michaelis Menten model following an ordered mechanism without products formulated via the steady state assumption"@en

Bi Bi Reaction Ordered Mechanism ODE Systemni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionOrderedMechansimODESystem

ODE System describing a Bi Bi Reaction with an Ordered mechanism over time
belongs to
Mathematical Formulation c
has facts
contains formulation op Enzyme - Product 1 - Product 2 - Complex Concentration ODE (Bi Bi Reaction Ordered) ni
contains formulation op Enzyme - Product 1 - Complex Concentration ODE (Bi Bi Reaction Ordered) ni
contains formulation op Enzyme - Substrate 1 - Substrate 2 - Complex Concentration ODE (Bi Bi Reaction Ordered) ni
contains formulation op Enzyme - Substrate 1 - Complex Concentration ODE (Bi Bi Reaction Ordered) ni
contains formulation op Enzyme Concentration ODE (Bi Bi Reaction Ordered) ni
contains formulation op Product 1 Concentration ODE (Bi Bi Reaction Ordered) ni
contains formulation op Product 2 Concentration ODE (Bi Bi Reaction Ordered) ni
contains formulation op Substrate 1 Concentration ODE (Bi Bi Reaction Ordered) ni
contains formulation op Substrate 2 Concentration ODE (Bi Bi Reaction Ordered) ni
contains quantity op Enzyme Concentration ni
contains quantity op Enzyme - Product 1 Complex Concentration ni
contains quantity op Enzyme - Product 1 - Product 2 Complex Concentration ni
contains quantity op Enzyme - Substrate 1 Complex Concentration ni
contains quantity op Enzyme - Substrate 1 - Substrate 2 Complex Concentration ni
contains quantity op Product 1 Concentration ni
contains quantity op Product 2 Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate of Enzyme ni
contains quantity op Reaction Rate of Enzyme - Product 1 Complex ni
contains quantity op Reaction Rate of Enzyme - Product 1 - Product 2 Complex ni
contains quantity op Reaction Rate of Enzyme - Substrate 1 Complex ni
contains quantity op Reaction Rate of Enzyme - Substrate 1 - Substrate 2 Complex ni
contains quantity op Reaction Rate of Product 1 ni
contains quantity op Reaction Rate of Product 2 ni
contains quantity op Reaction Rate of Substrate 1 ni
contains quantity op Reaction Rate of Substrate 2 ni
contains quantity op Substrate 1 Concentration ni
contains quantity op Substrate 2 Concentration ni
contains quantity op Time ni
defining formulation dp "$\begin{align} \frac{dc_{S_1}}{dt} &= k_{-1} * c_{ES_1} - k_{1} * c_{E} * c_{S_1} \\ \frac{dc_{S_2}}{dt} &= k_{-2} * c_{ES_{1}S_{2}} - k_{2} * c_{ES_1} * c_{S_2} \\ \frac{dc_{ES_1}}{dt} &= k_{1} * c_{E} * c_{S_1} + k_{-2} * c_{ES_{1}S_{2}} - k_{-1} * c_{ES_1} - k_2 * c_{ES_1} * c_{S_2} \\ \frac{dc_{ES_{1}S_{2}}}{dt} &= k_{2} * c_{ES_1} * c_{S_2} + k_{-3} * c_{EP_{1}P_{2}} - k_{-2} * c_{ES_{1}S_{2}} - k_{3} * c_{ES_{1}S_{2}} \\ \frac{dc_{EP_{1}P_{2}}}{dt} &= k_{3} * c_{ES_{1}S_{2}} + k_{-4} * c_{EP_1} * c_{P_2} - k_{-3} * c_{EP_{1}P_{2}} - k_{4} * c_{EP_{1}P_{2}} \\ \frac{dc_{EP_1}}{dt} &= k_{4} * c_{EP_{1}P_{2}} + k_{-5} * c_{E} * c_{P_1} - k_{-4} * c_{EP_1} * c_{P_2} - k_{5} * c_{EP_1} \\ \frac{dc_{P_1}}{dt} &= k_{5} * c_{EP_1} - k_{-5} * c_{E} * c_{P_1} \\ \frac{dc_{P_2}}{dt} &= k_{4} * c_{EP_{1}P_{2}} - k_{-4} * c_{EP_1} * c_{P_2} \\ \frac{dc_{E}}{dt} &= k_{-1} * c_{ES_1} + k_5 * c_{EP_1} - k_{1} * c_{E} * c_{S_1} - k_{-5} * c_{E} * c_{P_1} \\ \end{align}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{EP_1P_2}}{dt}$, Reaction Rate of Enzyme - Product 1 - Product 2 Complex"^^La Te X ep
in defining formulation dp "$\frac{dc_{EP_1}}{dt}$, Reaction Rate of Enzyme - Product 1 Complex"^^La Te X ep
in defining formulation dp "$\frac{dc_{ES_1S_2}}{dt}$, Reaction Rate of Enzyme - Substrate 1 - Substrate 2 Complex"^^La Te X ep
in defining formulation dp "$\frac{dc_{ES_1}}{dt}$, Reaction Rate of Enzyme - Substrate 1 Complex"^^La Te X ep
in defining formulation dp "$\frac{dc_{E}}{dt}$, Reaction Rate of Enzyme"^^La Te X ep
in defining formulation dp "$\frac{dc_{P_1}}{dt}$, Reaction Rate of Product 1"^^La Te X ep
in defining formulation dp "$\frac{dc_{P_2}}{dt}$, Reaction Rate of Product 2"^^La Te X ep
in defining formulation dp "$\frac{dc_{S_1}}{dt}$, Reaction Rate of Substrate 1"^^La Te X ep
in defining formulation dp "$\frac{dc_{S_2}}{dt}$, Reaction Rate of Substrate 2"^^La Te X ep
in defining formulation dp "$c_{EP_1P_2}$, Enzyme - Product 1 - Product 2 Complex Concentration"^^La Te X ep
in defining formulation dp "$c_{EP_1}$, Enzyme - Product 1 Complex Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_1S_2}$, Enzyme - Substrate 1 - Substrate 2 Complex Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Enzyme - Substrate 1 Complex Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Enzyme Concentration"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Product 1 Concentration"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Product 2 Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Substrate 1 Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Substrate 2 Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-5}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{5}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Bi Bi Reaction Ordered Mechanism with single central Complex (ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionOrderedMechanismODEModelsingleCC

Ordinary differential equations for the rates of change of all chemical species (substrate 1 and 2, enzyme, enzyme - substrate 1 - complex, enzyme - substrate 1 - substrate 2 = enzyme - product 1 - product 2 - complex, enzyme - product 1 - complex and product 1 and 2 in a Bi Bi Reaction following the Ordered Mechanism with a single central Complex. k_{i} with positive or negative i represents the rate constant of the forward- or backward-reaction i-th reaction step.
belongs to
Mathematical Model c
has facts
applied by task op Parameter Estimation of Enzyme Kinetics ni
applied by task op Sensitivity Analysis of Complex Kinetic Systems ni
applied by task op Simulation of Complex Kinetic Systems ni
contains formulation op Bi Bi Reaction Ordered Mechanism with single central Complex ODE System ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Enzyme Concentration (Bi Bi Reaction Ordered - ODE Model) ni
contains initial condition op Initial Enzyme - Product 1 - Complex Concentration (Bi Bi Reaction Ordered - ODE Model) ni
contains initial condition op Initial Enzyme - Substrate 1 - Complex Concentration (Bi Bi Reaction Ordered - ODE Model) ni
contains initial condition op Initial Enzyme - Substrate 1 - Substrate 2 = Enzyme Product 1 - Product 2 - Complex Concentration (Bi Bi Reaction Ordered with single central Compelx - ODE Model) ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Ordered - ODE Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Ordered - ODE Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Ordered - ODE Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Ordered - ODE Model) ni
models op Bi Bi Reaction following Ordered Mechanism with single central complex ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "true"^^boolean
is linear dp "false"^^boolean
is time-continuous dp "true"^^boolean
description ap "bi bi reaction with single central complex model following an ordered mechanism"@en

Bi Bi Reaction Ordered Mechanism with single central Complex ODE Systemni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionOrderedMechansimODESystemsingleCC

ODE System describing a Bi Bi Reaction with an Ordered mechanism and a single central Complex over time
belongs to
Mathematical Formulation c
has facts
contains formulation op Enzyme - Product 1 - Complex Concentration ODE (Bi Bi Reaction Ordered with single central Complex) ni
contains formulation op Enzyme - Substrate 1 - Substrate 2 = Enzyme - Product 1 - Product 2 - Complex Concentration ODE (Bi Bi Reaction Ordered with single central Complex) ni
contains formulation op Enzyme - Substrate 1 - Complex Concentration ODE (Bi Bi Reaction Ordered with single central Complex) ni
contains formulation op Enzyme Concentration ODE (Bi Bi Reaction Ordered with single central Complex) ni
contains formulation op Product 1 Concentration ODE (Bi Bi Reaction Ordered with single central Complex) ni
contains formulation op Product 2 Concentration ODE (Bi Bi Reaction Ordered with single central Complex) ni
contains formulation op Substrate 1 Concentration ODE (Bi Bi Reaction Ordered with single central Complex) ni
contains formulation op Substrate 2 Concentration ODE (Bi Bi Reaction Ordered with single central Complex) ni
contains quantity op Enzyme Concentration ni
contains quantity op Enzyme - Product 1 Complex Concentration ni
contains quantity op Enzyme - Substrate 1 Complex Concentration ni
contains quantity op Enzyme - Substrate 1 - Substrate 2 = Enzyme - Product 1 - Product 2 Complex Concentration ni
contains quantity op Product 1 Concentration ni
contains quantity op Product 2 Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate of Enzyme ni
contains quantity op Reaction Rate of Enzyme - Substrate 1 Complex ni
contains quantity op Reaction Rate of Product 1 ni
contains quantity op Reaction Rate of Product 2 ni
contains quantity op Reaction Rate of Substrate 1 ni
contains quantity op Reaction Rate of Substrate 2 ni
contains quantity op Reaction Rate of Enzyme - Substrate 1 - Substrate 2 = Enzyme - Product 1 - Product 2 Complex ni
contains quantity op Substrate 1 Concentration ni
contains quantity op Substrate 2 Concentration ni
contains quantity op Time ni
defining formulation dp "$\begin{align} \frac{dc_{S_1}}{dt} &= k_{-1} * c_{ES_1} - k_{1} * c_{E} * c_{S_1} \\ \frac{dc_{S_2}}{dt} &= k_{-2} * c_{ES_{1}S_{2}=EP_{1}P_{2}} - k_{2} * c_{ES_1} * c_{S_2} \\ \frac{dc_{ES_1}}{dt} &= k_{1} * c_{E} * c_{S_1} + k_{-2} * c_{ES_{1}S_{2}=EP_{1}P_{2}} - k_{-1} * c_{ES_1} - k_2 * c_{ES_1} * c_{S_2} \\ \frac{dc_{ES_{1}S_{2}=EP_{1}P_{2}}}{dt} &= k_{2} * c_{ES_1} * c_{S_2} - k_{-2} * c_{ES_{1}S_{2}=EP_{1}P_{2}} + k_{-4} * c_{EP_1} * c_{P_2} - k_{4} * c_{ES_{1}S_{2}=EP_{1}P_{2}} \\ \frac{dc_{EP_1}}{dt} &= k_{4} * c_{ES_{1}S_{2}=EP_{1}P_{2}} + k_{-5} * c_{E} * c_{P_1} - k_{-4} * c_{EP_1} * c_{P_2} - k_{5} * c_{EP_1} \\ \frac{dc_{P_1}}{dt} &= k_{5} * c_{EP_1} - k_{-5} * c_{E} * c_{P_1} \\ \frac{dc_{P_2}}{dt} &= k_{4} * c_{ES_{1}S_{2}=EP_{1}P_{2}} - k_{-4} * c_{EP_1} * c_{P_2} \\ \frac{dc_{E}}{dt} &= k_{-1} * c_{ES_1} + k_5 * c_{EP_1} - k_{1} * c_{E} * c_{S_1} - k_{-5} * c_{E} * c_{P_1} \\ \end{align}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{EP_1}}{dt}$, Reaction Rate of Enzyme - Product 1 Complex"^^La Te X ep
in defining formulation dp "$\frac{dc_{ES_1}}{dt}$, Reaction Rate of Enzyme - Substrate 1 Complex"^^La Te X ep
in defining formulation dp "$\frac{dc_{ES_{1}S_{2}=EP_{1}P_{2}}}{dt}$, Reaction Rate of Enzyme - Substrate 1 - Substrate 2 = Enzyme - Product 1 - Product 2 Complex"^^La Te X ep
in defining formulation dp "$\frac{dc_{E}}{dt}$, Reaction Rate of Enzyme"^^La Te X ep
in defining formulation dp "$\frac{dc_{P_1}}{dt}$, Reaction Rate of Product 1"^^La Te X ep
in defining formulation dp "$\frac{dc_{P_2}}{dt}$, Reaction Rate of Product 2"^^La Te X ep
in defining formulation dp "$\frac{dc_{S_1}}{dt}$, Reaction Rate of Substrate 1"^^La Te X ep
in defining formulation dp "$\frac{dc_{S_2}}{dt}$, Reaction Rate of Substrate 2"^^La Te X ep
in defining formulation dp "$c_{EP_1}$, Enzyme - Product 1 Complex Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Enzyme - Substrate 1 Complex Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_{1}S_{2}=EP_{1}P_{2}}$, Enzyme - Substrate 1 - Substrate 2 = Enzyme - Product 1 - Product 2 Complex Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Enzyme Concentration"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Product 1 Concentration"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Product 2 Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Substrate 1 Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Substrate 2 Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-5}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{5}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Bi Bi Reaction Ping Pong Mechanism (ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionPingPongMechansimODEModel

Ordinary differential equations for the rates of change of all chemical species (substrate 1 and 2, enzyme, enzyme - substrate 1 - complex, intermediate, intermediate - substrate 2 - complex, product 1 and 2) in a Bi Bi Reaction following the Ping Pong Mechanism. $k_{i}$ with positive or negative i represents the rate constant of the forward- or backward-reaction i-th reaction step.
belongs to
Mathematical Model c
has facts
applied by task op Parameter Estimation of Enzyme Kinetics ni
applied by task op Sensitivity Analysis of Complex Kinetic Systems ni
applied by task op Simulation of Complex Kinetic Systems ni
contains formulation op Bi Bi Reaction Ping Pong Mechanism ODE System ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Enzyme Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
contains initial condition op Initial Enzyme - Substrate 1 - Complex Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
contains initial condition op Initial Intermediate Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
contains initial condition op Initial Intermediate - Substrate 2 - Complex Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
models op Bi Bi Reaction following Ping Pong Mechanism ni
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "true"^^boolean
is linear dp "false"^^boolean
is time-continuous dp "true"^^boolean
description ap "bi bi reaction model following a ping-pong mechanism"@en

Bi Bi Reaction Ping Pong Mechanism Michaelis Menten Model with Product 1 (Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionPingPongMechanismMichaelisMentenModelwithProduct1SS

belongs to
Mathematical Model c
has facts
applied by task op Parameter Estimation of Enzyme Kinetics ni
applied by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains formulation op Michaelis Menten Equation (Bi Bi Reaction Ping Pong with Product 1 - Michaelis Menten Model - Steady State Assumption) ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Ping Pong with Product 1 - Michaelis Menten Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Ping Pong without Product 2 - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model) ni
generalized by model op Bi Bi Reaction Ping Pong Mechanism Michaelis Menten Model with Products 1 and 2 (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ping Pong Mechanism (ODE Model) ni
models op Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism with Product 1 ni
similar to model op Bi Bi Reaction Ping Pong Mechanism Michaelis Menten Model with Product 2 (Steady State Assumption) ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean
description ap "bi bi reaction Michaelis Menten model following a ping-pong mechanism with product 1 formulated via the steady state assumption"@en

Bi Bi Reaction Ping Pong Mechanism Michaelis Menten Model with Product 2 (Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionPingPongMechanismMichaelisMentenModelwithProduct2SS

belongs to
Mathematical Model c
has facts
applied by task op Parameter Estimation of Enzyme Kinetics ni
applied by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains formulation op Michaelis Menten Equation (Bi Bi Reaction Ping Pong with Product 2 - Michaelis Menten Model - Steady State Assumption) ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Ping Pong without Product 1 - Michaelis Menten Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Ping Pong with Product 2 - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model) ni
generalized by model op Bi Bi Reaction Ping Pong Mechanism Michaelis Menten Model with Products 1 and 2 (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ping Pong Mechanism (ODE Model) ni
models op Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism with Product 2 ni
similar to model op Bi Bi Reaction Ping Pong Mechanism Michaelis Menten Model with Product 1 (Steady State Assumption) ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean
description ap "bi bi reaction Michaelis Menten model following a ping-pong mechanism with product 2 formulated via the steady state assumption"@en

Bi Bi Reaction Ping Pong Mechanism Michaelis Menten Model with Products 1 and 2 (Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionPingPongMechanismMichaelisMentenModelwithProducts1and2SS

belongs to
Mathematical Model c
has facts
applied by task op Parameter Estimation of Enzyme Kinetics ni
applied by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains formulation op Michaelis Menten Equation (Bi Bi Reaction Ping Pong with Products 1 and 2 - Michaelis Menten Model - Steady State Assumption) ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Ping Pong with Product 1 - Michaelis Menten Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Ping Pong with Product 2 - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model) ni
generalized by model op Bi Bi Reaction Ping Pong Mechanism (ODE Model) ni
models op Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism with Products 1 and 2 ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean
description ap "bi bi reaction Michaelis Menten model following a ping-pong mechanism with products 1 and 2 formulated via the steady state assumption"@en

Bi Bi Reaction Ping Pong Mechanism Michaelis Menten Model without Products (Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionPingPongMechanismMichaelisMentenModelwithoutProductsSS

belongs to
Mathematical Model c
has facts
applied by task op Parameter Estimation of Enzyme Kinetics ni
applied by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains formulation op Michaelis Menten Equation (Bi Bi Reaction Ping Pong without Products - Michaelis Menten Model - Steady State Assumption) ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Ping Pong without Product 1 - Michaelis Menten Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Ping Pong without Product 2 - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model) ni
generalized by model op Bi Bi Reaction Ping Pong Mechanism Michaelis Menten Model with Product 1 (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ping Pong Mechanism Michaelis Menten Model with Product 2 (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ping Pong Mechanism Michaelis Menten Model with Products 1 and 2 (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ping Pong Mechanism (ODE Model) ni
models op Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism without Products ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean
description ap "bi bi reaction Michaelis Menten model following a ping-pong mechanism without products formulated via the steady state assumption"@en

Bi Bi Reaction Ping Pong Mechanism ODE Systemni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionPingPongMechansimODESystem

ODE System describing a Bi Bi Reaction with a Ping Pong mechanism over time
belongs to
Mathematical Formulation c
has facts
contains formulation op Enzyme - Substrate 1 - Complex Concentration ODE (Bi Bi Reaction Ping Pong) ni
contains formulation op Enzyme Concentration ODE (Bi Bi Reaction Ping Pong) ni
contains formulation op Intermediate Concentration ODE (Bi Bi Reaction Ping Pong) ni
contains formulation op Intermediate - Substrate 2 - Complex Concentration ODE (Bi Bi Reaction Ping Pong) ni
contains formulation op Product 1 Concentration ODE (Bi Bi Reaction Ping Pong) ni
contains formulation op Product 2 Concentration ODE (Bi Bi Reaction Ping Pong) ni
contains formulation op Substrate 1 Concentration ODE (Bi Bi Reaction Ping Pong) ni
contains formulation op Substrate 2 Concentration ODE (Bi Bi Reaction Ping Pong) ni
contains quantity op Enzyme Concentration ni
contains quantity op Enzyme - Substrate 1 Complex Concentration ni
contains quantity op Intermediate Concentration ni
contains quantity op Intermediate - Substrate 2 Complex Concentration ni
contains quantity op Product 1 Concentration ni
contains quantity op Product 2 Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate of Enzyme ni
contains quantity op Reaction Rate of Enzyme - Substrate 1 Complex ni
contains quantity op Reaction Rate of Intermediate ni
contains quantity op Reaction Rate of Intermediate - Substrate 2 Complex ni
contains quantity op Reaction Rate of Product 1 ni
contains quantity op Reaction Rate of Product 2 ni
contains quantity op Reaction Rate of Substrate 1 ni
contains quantity op Reaction Rate of Substrate 2 ni
contains quantity op Substrate 1 Concentration ni
contains quantity op Substrate 2 Concentration ni
contains quantity op Time ni
defining formulation dp "$\begin{align} \frac{dc_{S_1}}{dt} &= k_{-1} * c_{ES_1} - k_{1} * c_{E} * c_{S_1} \\ \frac{dc_{S_2}}{dt} &= k_{-3} * c_{E*S_2} - k_{3} * c_{E*} * c_{S_2} \\ \frac{dc_{E}}{dt} &= k_{-1} * c_{ES_1} + k_{4} * c_{E*S_2} - k_{1} * c_{E} * c_{S_1} - k_{-4} * c_{E} * c_{P_2} \\ \frac{dc_{ES_1}}{dt} &= k_{1} * c_{E} * c_{S_1} + k_{-2} * c_{E*} * c_{P_1} - k_{-1} * c_{ES_1} - k_{2} c_{ES_1} \\ \frac{dc_{E*}}{dt} &= k_{2} * c_{ES_1} + k_{-3} * c_{E*S_2} - k_{-2} * c_{E*} * c_{P_1} - k_{3} * c_{E*} * c_{S_2} \\ \frac{dc_{E*S_2}}{dt} &= k_{3} * c_{E*} * c_{S_2} + k_{-4} * c_{E} * c_{P_2} - k_{-3} * c_{E*S_2} - k_{4} * c_{E*S_2} \\ \frac{dc_{P_1}}{dt} &= k_{2} * c_{ES_1} - k_{-2} * c_{E*} * c_{P_1} \\ \frac{dc_{P_2}}{dt} &= k_{4} * c_{E*S_2} - k_{-4} * c_{P_2} * c_{E} \\ \end{align}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{E*S_2}}{dt}$, Reaction Rate of Intermediate - Substrate 2 Complex"^^La Te X ep
in defining formulation dp "$\frac{dc_{E*}}{dt}$, Reaction Rate of Intermediate"^^La Te X ep
in defining formulation dp "$\frac{dc_{ES_1}}{dt}$, Reaction Rate of Enzyme - Substrate 1 Complex"^^La Te X ep
in defining formulation dp "$\frac{dc_{E}}{dt}$, Reaction Rate of Enzyme"^^La Te X ep
in defining formulation dp "$\frac{dc_{P_1}}{dt}$, Reaction Rate of Product 1"^^La Te X ep
in defining formulation dp "$\frac{dc_{P_2}}{dt}$, Reaction Rate of Product 2"^^La Te X ep
in defining formulation dp "$\frac{dc_{S_1}}{dt}$, Reaction Rate of Substrate 1"^^La Te X ep
in defining formulation dp "$\frac{dc_{S_2}}{dt}$, Reaction Rate of Substrate 2"^^La Te X ep
in defining formulation dp "$c_{E*S_2}$, Intermediate - Substrate 2 Complex Concentration"^^La Te X ep
in defining formulation dp "$c_{E*}$, Intermediate Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Enzyme - Substrate 1 Complex Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Enzyme Concentration"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Product 1 Concentration"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Product 2 Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Substrate 1 Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Substrate 2 Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Bi Bi Reaction Theorell-Chance Mechanism (ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionTheorellChanceMechansimODEModel

Ordinary differential equations for the rates of change of all chemical species (substrate 1 and 2, enzyme, enzyme - substrate 1 - complex, enzyme - product 2 - complex, product 1 and 2) in a Bi Bi Reaction following the Theorell-Chance Mechanism. $k_{i}$ with positive or negative i represents the rate constant of the forward- or backward-reaction i-th reaction step.
belongs to
Mathematical Model c
has facts
applied by task op Parameter Estimation of Enzyme Kinetics ni
applied by task op Sensitivity Analysis of Complex Kinetic Systems ni
applied by task op Simulation of Complex Kinetic Systems ni
contains formulation op Bi Bi Reaction Theorell-Chance Mechanism ODE System ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Enzyme Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni
contains initial condition op Initial Enzyme - Product 2 - Complex Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni
contains initial condition op Initial Enzyme - Substrate 1 - Complex Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni
models op Bi Bi Reaction following Theorell-Chance Mechanism ni
description ap "bi bi reaction model following a Theorell-Chance mechanism"@en

Bi Bi Reaction Theorell-Chance Mechanism Michaelis Menten Model with Product 1 (Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionTheorellChanceMechanismMichaelisMentenModelwithProduct1SS

belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Theorell-Chance with Product 1 - Michaelis Menten Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Theorell-Chance without Product 2 - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model) ni
generalized by model op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Products 1 and 2 (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ordered Mechanism (ODE Model) ni
generalizes model op Bi Bi Reaction Theorell-Chance Mechanism Michaelis Menten Model without Products (Steady State Assumption) ni
models op Initial Reaction Rate of Bi Bi Reaction following Theorell-Chance Mechanism with Product 1 ni
similar to model op Bi Bi Reaction Theorell-Chance Mechanism Michaelis Menten Model with Product 2 (Steady State Assumption) ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean
description ap "bi bi reaction Michaelis Menten model following a Theorell-Chance mechanism with product 1 formulated via the steady state assumption"@en

Bi Bi Reaction Theorell-Chance Mechanism Michaelis Menten Model with Product 2 (Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionTheorellChanceMechanismMichaelisMentenModelwithProduct2SS

belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Theorell-Chance without Product 1 - Michaelis Menten Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Theorell-Chance with Product 2 - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model) ni
generalized by model op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Products 1 and 2 (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ordered Mechanism (ODE Model) ni
generalizes model op Bi Bi Reaction Theorell-Chance Mechanism Michaelis Menten Model without Products (Steady State Assumption) ni
models op Initial Reaction Rate of Bi Bi Reaction following Theorell-Chance Mechanism with Product 2 ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean
description ap "bi bi reaction Michaelis Menten model following a Theorell-Chance mechanism with product 2 formulated via the steady state assumption"@en

Bi Bi Reaction Theorell-Chance Mechanism Michaelis Menten Model with Products 1 and 2 (Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionTheorellChanceMechanismMichaelisMentenModelwithProducts1and2SS

belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Theorell-Chance with Product 1 - Michaelis Menten Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Theorell-Chance with Product 2 - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model) ni
generalized by model op Bi Bi Reaction Ordered Mechanism (ODE Model) ni
models op Initial Reaction Rate of Bi Bi Reaction following Theorell-Chance Mechanism withs Product 1 and 2 ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean
description ap "bi bi reaction Michaelis Menten model following a Theorell-Chance mechanism with products 1 and 2 formulated via the steady state assumption"@en

Bi Bi Reaction Theorell-Chance Mechanism Michaelis Menten Model without Products (Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionTheorellChanceMechanismMichaelisMentenModelwithoutProductsSS

belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Product 1 Concentration (Bi Bi Reaction Theorell-Chance without Product 1 - Michaelis Menten Model) ni
contains initial condition op Initial Product 2 Concentration (Bi Bi Reaction Theorell-Chance without Product 2 - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 1 Concentration (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model) ni
contains initial condition op Initial Substrate 2 Concentration (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model) ni
generalized by model op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Product 1 (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Product 2 (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Products 1 and 2 (Steady State Assumption) ni
generalized by model op Bi Bi Reaction Ordered Mechanism (ODE Model) ni
models op Initial Reaction Rate of Bi Bi Reaction following Theorell-Chance Mechanism without Products ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean
description ap "bi bi reaction Michaelis Menten model following a Theorell-Chance mechanism without products formulated via the steady state assumption"@en

Bi Bi Reaction Theorell-Chance Mechanism ODE Systemni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BiBiReactionTheorellChanceMechansimODESystem

ODE System describing a Bi Bi Reaction with an Ordered mechanism over time
belongs to
Mathematical Formulation c
has facts
contains formulation op Enzyme - Product 2 - Complex Concentration ODE (Bi Bi Reaction Theorell-Chance) ni
contains formulation op Enzyme - Substrate 1 - Complex Concentration ODE (Bi Bi Reaction Theorell-Chance) ni
contains formulation op Enzyme Concentration ODE (Bi Bi Reaction Theorell-Chance) ni
contains formulation op Product 1 Concentration ODE (Bi Bi Reaction Theorell-Chance) ni
contains formulation op Product 2 Concentration ODE (Bi Bi Reaction Theorell-Chance) ni
contains formulation op Substrate 1 Concentration ODE (Bi Bi Reaction Theorell-Chance) ni
contains formulation op Substrate 2 Concentration ODE (Bi Bi Reaction Theorell-Chance) ni
contains quantity op Enzyme Concentration ni
contains quantity op Enzyme - Product 2 Complex Concentration ni
contains quantity op Enzyme - Substrate 1 Complex Concentration ni
contains quantity op Product 1 Concentration ni
contains quantity op Product 2 Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate of Enzyme ni
contains quantity op Reaction Rate of Enzyme - Product 2 Complex ni
contains quantity op Reaction Rate of Enzyme - Substrate 1 Complex ni
contains quantity op Reaction Rate of Product 1 ni
contains quantity op Reaction Rate of Product 2 ni
contains quantity op Reaction Rate of Substrate 1 ni
contains quantity op Reaction Rate of Substrate 2 ni
contains quantity op Substrate 1 Concentration ni
contains quantity op Substrate 2 Concentration ni
contains quantity op Time ni
defining formulation dp "$\begin{align*} \frac{dc_{S_1}}{dt} &= k_{-1} * c_{ES_1} - k_{1} * c_{E} * c_{S_1} \\ \frac{dc_{S_2}}{dt} &= k_{-2} * c_{EP_2} * c_{P_1} - k_{2} * c_{ES_1} * c_{S_2} \\ \frac{dc_{P_1}}{dt} &= k_{2} * c_{ES_1} * c_{S_2} - k_{-2} * c_{EP_2} * c_{P_1} \\ \frac{dc_{P_2}}{dt} &= k_{3} * c_{EP_2} - k_{-3} * c_{E} * c_{P_2} \\ \frac{dc_{ES_1}}{dt} &= k_{1} * c_{E} * c_{S_1} + k_{-2} * c_{EP_{2}} * c_{P_1} - k_{-1} * c_{ES_1} - k_2 * c_{ES_1} * c_{S_2} \\ \frac{dc_{EP_2}}{dt} &= k_{2} * c_{ES_1} * c_{S_2} + k_{-3} * c_{E} * c_{P_2} - k_{-2} * c_{EP_2} * c_{P_1} - k_3 * c_{EP_2} \\ \frac{dc_{E}}{dt} &= k_{-1} * c_{ES_1} + k_3 * c_{EP_2} - k_{1} * c_{E} * c_{S_1} - k_{-3} * c_{E} * c_{P_2} \end{align*}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{EP_2}}{dt}$, Reaction Rate of Enzyme - Product 2 Complex"^^La Te X ep
in defining formulation dp "$\frac{dc_{ES_1}}{dt}$, Reaction Rate of Enzyme - Substrate 1 Complex"^^La Te X ep
in defining formulation dp "$\frac{dc_{E}}{dt}$, Reaction Rate of Enzyme"^^La Te X ep
in defining formulation dp "$\frac{dc_{P_1}}{dt}$, Reaction Rate of Product 1"^^La Te X ep
in defining formulation dp "$\frac{dc_{P_2}}{dt}$, Reaction Rate of Product 2"^^La Te X ep
in defining formulation dp "$\frac{dc_{S_1}}{dt}$, Reaction Rate of Substrate 1"^^La Te X ep
in defining formulation dp "$\frac{dc_{S_2}}{dt}$, Reaction Rate of Substrate 2"^^La Te X ep
in defining formulation dp "$c_{EP_2}$, Enzyme - Product 2 Complex Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Enzyme - Substrate 1 Complex Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Enzyme Concentration"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Product 1 Concentration"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Product 2 Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Substrate 1 Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Substrate 2 Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Biologyni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Biology

belongs to
Research Field c
has facts
description ap "scientific study of living things, especially their structure, function, growth, evolution, and distribution"@en
mardi I D ap Item: Q59666 ep
wikidata I D ap Q420 ep

Biomechanicsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Biomechanics

belongs to
Research Field c
has facts
contains problem op Muscle Movement ni
description ap "study of the structure and function of the mechanical aspects of biological systems"@en
wikidata I D ap Q193378 ep

Biophysicsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Biophysics

belongs to
Research Field c
has facts
generalized by field op Biology ni
generalizes field op Biomechanics ni
description ap "study of biological systems using methods from the physical sciences"@en
wikidata I D ap Q7100 ep

Birth Rateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BirthRate

Birth Rate to be used in the SIR and SIS Models with Births and Deaths. Note that, it is assumed that death rate = birth rate
belongs to
Quantity c
has facts
generalized by quantity op Rate ni
is dimensionless dp "false"^^boolean
description ap "total number of live births per 1,000 population divided by the length of a given period in years"@en
wikidata I D ap Q203516 ep

Bisswanger (2017) Enzyme Kineticsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Bisswanger_2017_Enzyme_Kinetics

belongs to
Publication c
has facts
surveys op Uni Uni Reaction Competitive Complete Inhibition (Dixon Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Competitive Complete Inhibition (Eadie Hofstee Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Competitive Complete Inhibition (Hanes Woolf Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Competitive Complete Inhibition (Lineweaver Burk Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Competitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Competitive Partial Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Mixed Complete Inhibition (Dixon Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Mixed Complete Inhibition (Eadie Hofstee Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Mixed Complete Inhibition (Hanes Woolf Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Mixed Complete Inhibition (Lineweaver Burk Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Mixed Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Mixed Partial Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Non-Competitive Complete Inhibition (Dixon Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Non-Competitive Complete Inhibition (Eadie Hofstee Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Non-Competitive Complete Inhibition (Hanes Woolf Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Non-Competitive Complete Inhibition (Lineweaver Burk Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Non-Competitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Non-Competitive Partial Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Uncompetitive Complete Inhibition (Dixon Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Uncompetitive Complete Inhibition (Eadie Hofstee Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Uncompetitive Complete Inhibition (Hanes Woolf Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Uncompetitive Complete Inhibition (Lineweaver Burk Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Uncompetitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
surveys op Uni Uni Reaction Uncompetitive Partial Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
doi I D ap 9783527806461 ep

Boltzmann Approximation For Electronsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BoltzmannApproximationForElectrons

belongs to
Mathematical Formulation c
has facts
contains quantity op Band Edge Energy For Conduction Band ni
contains quantity op Boltzmann Constant ni
contains quantity op Density Of Electrons ni
contains quantity op Density Of States For Conduction Band ni
contains quantity op Electric Potential ni
contains quantity op Elementary Charge ni
contains quantity op Fermi Potential For Electrons ni
contains quantity op Temperature ni
defining formulation dp "$n(\psi,\phi_n)=N_c\exp\left(\frac{q(\psi-\phi_n)-E_c}{k_BT}\right))$"^^La Te X ep
in defining formulation dp "$q$, Elementary Charge"
in defining formulation dp "$E_c$, Band Edge Energy For Conduction Band"^^La Te X ep
in defining formulation dp "$N_c$, Density Of States For Conduction Band"^^La Te X ep
in defining formulation dp "$T$, Temperature"^^La Te X ep
in defining formulation dp "$\phi_n$, Fermi Potential For Electrons"^^La Te X ep
in defining formulation dp "$\psi$, Electric Potential"^^La Te X ep
in defining formulation dp "$k_B$, Boltzmann Constant"^^La Te X ep
in defining formulation dp "$n$, Density Of Electrons"^^La Te X ep
is dynamic dp "false"^^boolean
is space-continuous dp "true"^^boolean
description ap "Boltzmann approximation for electrons; for use in semiconductor physics"@en

Boltzmann Approximation For Holesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BoltzmannApproximationForHoles

belongs to
Mathematical Formulation c
has facts
contains quantity op Band Edge Energy For Valence Band ni
contains quantity op Boltzmann Constant ni
contains quantity op Density Of Holes ni
contains quantity op Density Of States For Valence Band ni
contains quantity op Electric Potential ni
contains quantity op Elementary Charge ni
contains quantity op Fermi Potential For Holes ni
contains quantity op Temperature ni
defining formulation dp "$p(\psi,\phi_p)=N_v\exp\left(\frac{q(\phi_p-\psi)+E_v}{k_BT}\right)$"^^La Te X ep
in defining formulation dp "$q$, Elementary Charge"
in defining formulation dp "$E_v$, Band Edge Energy For Valence Band"^^La Te X ep
in defining formulation dp "$N_v$, Density Of States For Valence Band"^^La Te X ep
in defining formulation dp "$T$, Temperature"^^La Te X ep
in defining formulation dp "$\phi_p$, Fermi Potential For Holes"^^La Te X ep
in defining formulation dp "$\psi$, Electric Potential"^^La Te X ep
in defining formulation dp "$k_B$, Boltzmann Constant"^^La Te X ep
in defining formulation dp "$p$, Density Of Holes"^^La Te X ep
is dynamic dp "false"^^boolean
is space-continuous dp "true"^^boolean
description ap "Boltzmann approximation for holes; for use in semiconductor physics"@en

Boltzmann Constantni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BoltzmannConstant

belongs to
Quantity c
has facts
description ap "physical constant relating the average relative thermal energy with the thermodynamic temperature"@en
qudt I D ap Boltzmann Constant ep
wikidata I D ap Q5962 ep

Boolean Ringni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BooleanRing

belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
description ap "In mathematics, a ring that consists of only idempotent elements"@en
wikidata I D ap Q2634401 ep

Boolean Variableni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#BooleanVariable

data type that represents true or false values
belongs to
Quantity Kind c
has facts
generalizes quantity op Object Property ni
is dimensionless dp "true"^^boolean
wikidata I D ap Q520777 ep

Boundary Conditions of Electrophysiological Muscle ODE Systemni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Boundary_Conditions_for_Electrophysiological_Muscle_ODE_System

belongs to
Mathematical Formulation c
has facts
contained as boundary condition in op Electrophysiological Muscle ODE System ni
contains quantity op Displacement Muscle Tendon ni
contains quantity op Material Point Displacement ni
contains quantity op Material Point Velocity ni
contains quantity op Stress Tensor (Piola-Kirchhoff) ni
defining formulation dp "$$\begin{array}{cccc} \mathbf{x}_{\text{M}1} = \mathbf{x}_{\text{T}}, &\dot{\mathbf{x}}_{\text{M}1} = \dot{\mathbf{x}}_{\text{T}}, & \mathbf{P}(\mathbf{F}_{\text{M}1})=\mathbf{P}(\mathbf{F}_{\text{T}}), & \text{on $\partial \Omega_{\text{M}1-\text{T}}$} \\ \mathbf{x}_{\text{M}2} = \mathbf{x}_{\text{T}}, &\dot{\mathbf{x}}_{\text{M}2} = \dot{\mathbf{x}}_{\text{T}}, & \mathbf{P}(\mathbf{F}_{\text{M}2})=\mathbf{P}(\mathbf{F}_{\text{T}}), & \text{on $\partial \Omega_{\text{M}2-\text{T}}$} \end{array}$$"^^La Te X ep
in defining formulation dp "$\dot{\mathbf{x}}$, Material Point Velocity"^^La Te X ep
in defining formulation dp "$\mathbf{P}$, Stress Tensor (Piola-Kirchhoff)"^^La Te X ep
in defining formulation dp "$\mathbf{x}$, Material Point Displacement"^^La Te X ep
in defining formulation dp "$x$, Displacement Muscle Tendon"^^La Te X ep
description ap "kinematic and dynamic conditions at the interfaces beween each muscle and the tendon"@en

Briggs (1925) A note on the kinetics of enzyme actionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Briggs_1925_A_note_on_the_kinetics_of_enzyme_action

belongs to
Publication c
has facts
invents op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
doi I D ap bj0190338 ep

Celestial Mechanicsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#CelestialMechanics

Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, to produce ephemeris data.
belongs to
Research Field c
has facts
generalized by field op Astronomy ni
generalized by field op Classical Mechanics ni
description ap "branch of astronomy that deals with the motions of objects in outer space"@en
wikidata I D ap Q184274 ep

Center Of Provinceni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#CenterOfProvince

$\Omega^{(l)} \subset \Omega$. superscript (l) denotes the province
belongs to
Quantity c
has facts
description ap "centers of the respective provinces"@en

Centrifugal Distortion Constantni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#CentrifugalDistortionConstant

This distortion leads to changes in bond distance and angles, affecting the rotational spectrum.
belongs to
Quantity c
has facts
description ap "distortion of a molecule caused by the centrifugal force produced by rotation"@en

Change In Lengthni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ChangeInLength

belongs to
Quantity c
has facts
generalized by quantity op Length ni
description ap "difference between the current and the original (equilibrium) length"@en
wikidata I D ap Q91308394 ep

Change In Opinions Of Individualsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ChangeInOpinionsOfIndividuals

Individuals i = 1,...,N adapt their opinions in time according to this stochastic differential equation (SDE)
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Opinion Model With Influencers And Media ni
contains quantity op Interaction Force ni
contains quantity op Noise Strength ni
contains quantity op Opinion Vector of Individuals ni
contains quantity op Opinion Vector of Influencers ni
contains quantity op Opinion Vector of Media ni
contains quantity op Time ni
contains quantity op Wiener Process ni
defining formulation dp "$dx_i(t) = F_i(\mathbf{x}, \mathbf{y}, \mathbf{z}, t)dt + \sigma dW_i(t)$"^^La Te X ep
in defining formulation dp "$F_i(t)$, Interaction Force"^^La Te X ep
in defining formulation dp "$W_i(t)$, Wiener Process"^^La Te X ep
in defining formulation dp "$\mathbf{x}(t)$, Opinion Vector of Individuals"^^La Te X ep
in defining formulation dp "$\mathbf{y}(t)$, Opinion Vector of Media"^^La Te X ep
in defining formulation dp "$\mathbf{z}(t)$, Opinion Vector of Influencers"^^La Te X ep
in defining formulation dp "$\sigma$, Noise Strength"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is deterministic dp "false"^^boolean
is dimensionless dp "false"^^boolean
is space-continuous dp "true"^^boolean
is time-continuous dp "true"^^boolean

Change In Opinions Of Influencersni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ChangeInOpinionsOfInfluencers

Influencers l= 1,. . . , L slowly change their opinions in the direction of their average followership according to this Stochastic differential equation
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Opinion Model With Influencers And Media ni
contains quantity op Average Opinion Of Followers Of Influencers ni
contains quantity op Inertia Parameter For Opinion Changes Of Influencers ni
contains quantity op Noise Strength ni
contains quantity op Opinion ni
contains quantity op Time ni
contains quantity op Wiener Process ni
defining formulation dp "$\gamma d z_l(t)=\left(\hat{x}_l(t)-z_l(t)\right) d t+\hat{\sigma} d \hat{W}_l(t)$"^^La Te X ep
in defining formulation dp "$\gamma$, Inertia Parameter For Opinion Changes Of Influencers"^^La Te X ep
in defining formulation dp "$\hat{W}_l$, Wiener Process"^^La Te X ep
in defining formulation dp "$\hat{\sigma}$, Noise Strength"^^La Te X ep
in defining formulation dp "$\hat{x}_l(t)$, Average Opinion Of Followers Of Influencers"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$z_l(t)$, Opinion"^^La Te X ep
is deterministic dp "false"^^boolean
is dimensionless dp "false"^^boolean
is space-continuous dp "true"^^boolean

Change In Opinions Of Influencers In The Partial Mean Field Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ChangeInOpinionsOfInfluencrsInThePartialFieldModel

Stochastic Differential equation describing the change in opinions of a given Influencer in the partial field opinion model
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Partial Mean Field Opinion Model ni
contains quantity op Average Opinion Of Followers Of Influencers In The Partial Mean Field Model ni
contains quantity op Inertia Parameter For Opinion Changes Of Influencers ni
contains quantity op Noise Strength ni
contains quantity op Opinion ni
contains quantity op Time ni
contains quantity op Wiener Process ni
defining formulation dp "$\gamma d z_l(t)=\left(\hat{x}_l(t)-z_l(t)\right) d t+\hat{\sigma} d \hat{W}_l(t)$"^^La Te X ep
in defining formulation dp "$\gamma$, Inertia Parameter For Opinion Changes Of Influencers"^^La Te X ep
in defining formulation dp "$\hat{W}_l$, Wiener Process"^^La Te X ep
in defining formulation dp "$\hat{\sigma}$, Noise Strength"^^La Te X ep
in defining formulation dp "$\hat{x}_l$, Average Opinion Of Followers Of Infuencers In The Partial Field Model"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$z_l$, Opinion"^^La Te X ep
is deterministic dp "false"^^boolean

Change In Opinions Of Mediani back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ChangeInOpinionsOfMedia

media agents m = 1,...,M slowly adapt their opinions according to this stochastic differential equation such that media agents are drawn in the direction of the average opinion of their followers.
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Opinion Model With Influencers And Media ni
contains quantity op Average Opinion Of Followers Of Media ni
contains quantity op Inertia Parameter For Opinion Changes Of Media ni
contains quantity op Noise Strength ni
contains quantity op Opinion ni
contains quantity op Time ni
contains quantity op Wiener Process ni
defining formulation dp "$\Gamma d y_m(t)=\left(\tilde{x}_m(t)-y_m(t)\right) d t+\tilde{\sigma} d \tilde{W}_m(t)$"^^La Te X ep
in defining formulation dp "$\Gamma$, Inertia Parameter For Opinion Changes Of Media"^^La Te X ep
in defining formulation dp "$\tilde{W}_m$, Wiener Process"^^La Te X ep
in defining formulation dp "$\tilde{\sigma}$, Noise strength"^^La Te X ep
in defining formulation dp "$\tilde{x}_m(t)$, Average Opinion Of Followers Of Media"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$y_m(t)$, Opinion"^^La Te X ep
is deterministic dp "false"^^boolean
is dimensionless dp "false"^^boolean
is space-continuous dp "true"^^boolean

Change In Opinions Of Media In The Partial Mean Field Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ChangeInOpinionsOfMediaInThePartialFieldModel

Stochastic Differential equation describing the change in opinions of a given medium in the partial field opinion model
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Partial Mean Field Opinion Model ni
contains quantity op Average Opinion Of Followers Of Media In The Partial Mean Field Model ni
contains quantity op Inertia Parameter For Opinion Changes Of Media ni
contains quantity op Noise Strength ni
contains quantity op Opinion ni
contains quantity op Time ni
contains quantity op Wiener Process ni
defining formulation dp "$\Gamma d y_m(t)=\left(\tilde{x}_m(t)-y_m(t)\right) d t+\tilde{\sigma} d \tilde{W}_m(t)$"^^La Te X ep
in defining formulation dp "$\Gamma$, Inertia Parameter For Opinion Changes Of Media"^^La Te X ep
in defining formulation dp "$\tilde{W}_m$, Wiener Process"^^La Te X ep
in defining formulation dp "$\tilde{\sigma}$, Noise strength"^^La Te X ep
in defining formulation dp "$\tilde{x}_m$, Average Opinion Of Followers Of Media In The Partial Field Model"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$y_m$, Opinion"^^La Te X ep
is deterministic dp "false"^^boolean

Charge Transportni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ChargeTransport

belongs to
Research Problem c
has facts
contained in field op Continuum Mechanics ni
description ap "transport of electric charge"@en

Charge Transport Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ChargeTransportModel

belongs to
Mathematical Model c
has facts
contains formulation op Ohm Equation ni
models op Charge Transport ni
description ap "simple mathematical model for the transport of electric charge"@en

Chemical Potentialni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ChemicalPotential

e.g. in a chemical reaction or phase transition.
belongs to
Quantity c
has facts
generalizes quantity op External Chemical Potential ni
description ap "energy that can be absorbed or released due to a change of the particle number of a given species"@en
wikidata I D ap Q737004 ep

Chemical Reaction Kineticsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ChemicalReactionKinetics

belongs to
Research Field c
has facts
generalized by field op Physical Chemistry ni
generalizes field op Enzyme Kinetics ni
description ap "Teilgebiet der physikalischen Chemie, das die Geschwindigkeit chemischer Reaktionen untersucht"@de
description ap "study of the rates of chemical reactions"@en
wikidata I D ap Q209082 ep

Civil Engineeringni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Civil_Engineering

belongs to
Research Field c
has facts
description ap "engineering discipline specializing in design, construction and maintenance of the built environment"@en
wikidata I D ap Q77590 ep

Classical Accelerationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalAcceleration

belongs to
Quantity c
has facts
generalized by quantity op Acceleration ni
description ap "rate at which the magnitude and/or direction of velocity changes with time"@en
wikidata I D ap Q11376 ep

Classical Approximationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalApproximation

belongs to
Mathematical Formulation c
has facts
contained as assumption in op Classical Dynamics Model ni
contained as assumption in op Classical Hamilton Equations ni
contained as assumption in op Classical Newton Equation ni
contains quantity op de Broglie Wavelength ni
defining formulation dp "$\lambda \llt L$"^^La Te X ep
in defining formulation dp "$L$, typical dimension of the system"^^La Te X ep
in defining formulation dp "$\lambda$, de Broglie Wavelength"^^La Te X ep
description ap "classical dynamics as an approximation to quantum mechanics"@en

Classical Brownian Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalBrownianEquation

belongs to
Mathematical Formulation c
has facts
contains quantity op Boltzmann Constant ni
contains quantity op Classical Force ni
contains quantity op Classical Position ni
contains quantity op Diffusion Coefficient ni
contains quantity op Temperature ni
contains quantity op Time ni
contains quantity op White Noise ni
generalized by formulation op Classical Langevin Equation ni
defining formulation dp "$\frac{\text{d}}{\text{d}t}q = - \frac{D}{k_\text{B} T} F(q) + \sqrt{2 D} R(t)$"^^La Te X ep
in defining formulation dp "$D$, Diffusion Constant"^^La Te X ep
in defining formulation dp "$F$, Classical Force"^^La Te X ep
in defining formulation dp "$R(t)$, White Noise"^^La Te X ep
in defining formulation dp "$T$, Temperature"^^La Te X ep
in defining formulation dp "$k_\text{B}$, Boltzmann Constant"^^La Te X ep
in defining formulation dp "$q$, Classical Position"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is deterministic dp "false"^^boolean
is dynamic dp "true"^^boolean
description ap "special case of an equation of motion where no average acceleration takes place"@en
alt Label ap "Langevin Equation Without Inertia."@en
alt Label ap "Overdamped Langevin Equation"@en
wikidata I D ap Q178036 ep
wikidata I D ap Q4976526 ep

Classical Brownian Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalBrownianModel

Brownian dynamics is also known as overdamped Langevin dynamics.
belongs to
Mathematical Model c
has facts
contains formulation op Classical Brownian Equation ni
generalized by model op Classical Langevin Model ni
models op Molecular Dynamics ni
is deterministic dp "false"^^boolean
is dynamic dp "true"^^boolean
description ap "mathematical model for describing molecular systems in the diffusive regime"@en
wikidata I D ap Q4976526 ep

Classical Density (Phase Space)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalDensityPhaseSpace

The phase space distribution ρ ( p , q ) $\rho(p,q)$ determines the probability ρ ( p , q ) d n q d n p ${\displaystyle \rho (p,q)\;\mathrm {d} ^{n}q\,\mathrm {d} ^{n}p}$ that the system will be found in the infinitesimal phase space volume d n q d n p ${\displaystyle \mathrm {d} ^{n}q\,\mathrm {d} ^{n}p}$.
belongs to
Quantity c
has facts
generalized by quantity op Probability Distribution ni
generalized by quantity op Quantum Density Operator ni
description ap "probability that the system will be found in the infinitesimal phase space volume"@en

Classical Dynamics Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalDynamicsModel

belongs to
Mathematical Model c
has facts
contains formulation op Classical Hamilton Equations ni
contains formulation op Classical Newton Equation ni
contains initial condition op Initial Classical Momentum ni
contains initial condition op Initial Classical Position ni
models op Molecular Reaction Dynamics ni
models op Molecular Spectroscopy (Transient) ni
is space-continuous dp "true"^^boolean
is time-continuous dp "true"^^boolean
description ap "mathematical model of a system of point masses, subject to forces deriving from some potential energy function"@en

Classical Fokker Planck Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalFokkerPlanckEquation

For vanishing drift and constant diffusion, the Fokker Planck equation yield's Fick's first law of diffusion.
belongs to
Mathematical Formulation c
has facts
contains quantity op Classical Position ni
contains quantity op Control System Input ni
contains quantity op Diffusion Coefficient ni
contains quantity op Drift (Velocity) ni
contains quantity op Probability Distribution ni
contains quantity op Time ni
similar to formulation op Classical Brownian Equation ni
similar to formulation op Classical Langevin Equation ni
defining formulation dp "$\frac{\partial}{\partial t} p(x, t) = -\frac{\partial}{\partial x}\left[(\mu(x, t)-u) p(x, t)\right] + \frac{\partial^2}{\partial x^2}\left[D(x, t) p(x, t)\right]$"^^La Te X ep
in defining formulation dp "$D$, Diffusion constant"^^La Te X ep
in defining formulation dp "$\mu$, Drift"^^La Te X ep
in defining formulation dp "$p$, Probability Distribution"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$u_t$, Control System Input"^^La Te X ep
in defining formulation dp "$x$, Classical Position"^^La Te X ep
description ap "partial differential equation describing the dynamics of a probability density of the velocity of a particle under the influence of drag forces and random forces"
wikidata I D ap Q891766 ep

Classical Fokker Planck Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalFokkerPlanckModel

belongs to
Mathematical Model c
has facts
applied by task op Balanced Truncation (Bi-linear) ni
applied by task op H2 Optimal Approximation (Bi-linear) ni
applied by task op Optimal Control ni
contains formulation op Classical Fokker Planck Equation ni
similar to model op Classical Brownian Model ni
similar to model op Classical Langevin Model ni
description ap "dynamics of a probability density of the velocity of a particle under the influence of drag forces and random forces"@en
wikidata I D ap Q891766 ep

Classical Forceni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalForce

belongs to
Quantity c
has facts
contained in formulation op Classical Newton Equation ni
generalized by quantity op Force ni
description ap "vector quantity that describes the ability of an action to modify the movement and shape of an object"@en
wikidata I D ap Q11402 ep

Classical Hamilton Equationsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalHamiltonEquations

Hamiltonian mechanics emerged in 1833 as a reformulation of Lagrangian mechanics. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics replaces (generalized) velocities q ˙ i ${\displaystyle {\dot {q}}^{i}}$ used in Lagrangian mechanics with (generalized) momenta. Both theories provide interpretations of classical mechanics and describe the same physical phenomena.
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Classical Dynamics Model ni
contains quantity op Classical Hamilton Function ni
contains quantity op Classical Momentum ni
contains quantity op Classical Position ni
generalized by formulation op Schrödinger Equation (Time Dependent) ni
generalizes formulation op Classical Newton Equation ni
defining formulation dp "$\begin{align} \frac{\mathrm{d}\boldsymbol{q}}{\mathrm{d}t} &=& +\frac{\partial \mathcal{H}}{\partial \boldsymbol{p}} \\ \frac{\mathrm{d}\boldsymbol{p}}{\mathrm{d}t} &=& -\frac{\partial \mathcal{H}}{\partial \boldsymbol{q}} \end{align}$"^^La Te X ep
in defining formulation dp "$H$, Classical Hamilton Function"^^La Te X ep
in defining formulation dp "$p$, Classical Momentum"^^La Te X ep
in defining formulation dp "$q$, Classical Position"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is space-continuous dp "true"^^boolean
is time-continuous dp "true"^^boolean
description ap "classical equations of motion for systems described by a classical Hamiltoon function specifying the total energy"@en
wikidata I D ap Q1115699 ep

Classical Hamilton Equations (Leap Frog)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalHamiltonEquationsLeapFrog

belongs to
Mathematical Formulation c
has facts
contains formulation op Euler Forward Method ni
contains quantity op Classical Force ni
contains quantity op Classical Momentum ni
contains quantity op Classical Position ni
contains quantity op Mass ni
contains quantity op Time ni
contains quantity op Time Step ni
discretizes formulation op Classical Hamilton Equations ni
similar to formulation op Schrödinger Equation (Strang-Marchuk) ni
defining formulation dp "$\begin{align} p(t+\tau/2) &=& p(t)+\tau F(q(t))/2 \\ q(t+\tau) &=& q(t)+\tau p(t+\tau/2)/m \\ p(t+\tau) &=& p(t+\tau/2)+\tau F(q(t+\tau))/2 \end{align}$"^^La Te X ep
in defining formulation dp "$F$, Classical Forces"^^La Te X ep
in defining formulation dp "$\tau$, Time Step"^^La Te X ep
in defining formulation dp "$m$, Mass"^^La Te X ep
in defining formulation dp "$p$, Classical Momentum"^^La Te X ep
in defining formulation dp "$q$, Classical Position"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is time-continuous dp "false"^^boolean
description ap "leap frog scheme for time-discretization of Hamilton's equations of motion"@en

Classical Hamilton Functionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalHamiltonFunction

belongs to
Quantity c
has facts
contained in formulation op Classical Hamilton Equations ni
generalized by quantity op Energy ni
description ap "function of generalized positions and momenta in Hamiltonian mechanics, specifying the total energy of a system"@en
wikidata I D ap Q360356 ep

Classical Langevin Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalLangevinEquation

Note that a Langevin equation can be reformulated as a Fokker–Planck equation governing a probability distribution
belongs to
Mathematical Formulation c
has facts
contains quantity op Boltzmann Constant ni
contains quantity op Classical Force ni
contains quantity op Classical Position ni
contains quantity op Friction Coefficient ni
contains quantity op Mass ni
contains quantity op Temperature ni
contains quantity op Time ni
contains quantity op White Noise ni
generalizes formulation op Classical Newton Equation ni
defining formulation dp "$M\frac{\mathrm{d^2}}{\mathrm{d}t^2} \vec{q} = F(q) - \gamma \frac{\mathrm{d}}{\mathrm{d}t}{q} + \sqrt{2 \gamma k_B T} R(t)$"^^La Te X ep
in defining formulation dp "$F$, Classical Force"^^La Te X ep
in defining formulation dp "$M$, Mass"^^La Te X ep
in defining formulation dp "$R(t)$, White Noise"^^La Te X ep
in defining formulation dp "$T$, Temperature"^^La Te X ep
in defining formulation dp "$\gamma$, Friction Coefficient"^^La Te X ep
in defining formulation dp "$k_B$, Boltzmann Constant"^^La Te X ep
in defining formulation dp "$q$, Classical Position"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is deterministic dp "false"^^boolean
is dynamic dp "true"^^boolean
description ap "same as (classical) Newton's equation of motion, but with additional terms for friction|damping and for stochastic collisions added"@en
wikidata I D ap Q584537 ep

Classical Langevin Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalLangevinModel

The approach is characterized by the use of simplified models while accounting for omitted degrees of freedom only implicitly, i.e., by the use of stochastic differential equations.
belongs to
Mathematical Model c
has facts
contains formulation op Classical Langevin Equation ni
generalizes model op Classical Dynamics Model ni
is deterministic dp "false"^^boolean
is dynamic dp "true"^^boolean
description ap "mathematical model typically used to describe the dynamics of systems subject to a combination of deterministic and fluctuating forces"@en
wikidata I D ap Q6485978 ep

Classical Liouville Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalLiouvilleEquation

Consider a Hamiltonian dynamical system with canonical coordinates q i and conjugate momenta p i. Then the phase space distribution determines the probability $\rho ( p , q ) d n q d n p$ that the system will be found in the infinitesimal phase space volume $d n q d n p$ The Liouville equation governs the evolution of $\rho ( p , q ; t ) \rho(p,q;t)$ in time $t$
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Classical Dynamics Model ni
contains assumption op Classical Approximation ni
contains assumption op Nonrelativistic Approximation ni
contains quantity op Classical Density (Phase Space) ni
contains quantity op Classical Hamilton Function ni
contains quantity op Classical Momentum ni
contains quantity op Classical Position ni
contains quantity op Time ni
generalized by formulation op Quantum Liouville Equation ni
generalizes formulation op Classical Hamilton Equations ni
similar to formulation op Quantum Liouville Equation ni
defining formulation dp "$\frac{d\rho}{dt}=\frac{\partial\rho}{\partial t}+\sum_{i=1}^n\left(\frac{\partial\rho}{\partial q_i}\dot{q}_i+\frac{\partial\rho}{\partial p_i}\dot{p}_i\right)$"^^La Te X ep
in defining formulation dp "$H$, Classical Hamilton Function"^^La Te X ep
in defining formulation dp "$\rho$, Classical Density (Phase Space)'"^^La Te X ep
in defining formulation dp "$p$, Classical Momentum"^^La Te X ep
in defining formulation dp "$q$, Classical Position"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
description ap "partial differential equation for the that time rate of change of density of points in phase space"@en
wikidata I D ap Q766722 ep

Classical Mechanicsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalMechanics

belongs to
Research Field c
has facts
generalized by field op Continuum Mechanics ni
description ap "sub-field of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces"@en
wikidata I D ap Q11397 ep

Classical Momentumni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalMomentum

belongs to
Quantity c
has facts
contained in formulation op Classical Hamilton Equations ni
generalized by quantity op Momentum ni
description ap "momentum of a point particle in classical mechanics"@en
wikidata I D ap Q41273 ep

Classical Momentum (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalMomentumDefinition

belongs to
Mathematical Formulation c
has facts
contains quantity op Classical Momentum ni
contains quantity op Classical Velocity ni
contains quantity op Mass ni
defines op Classical Momentum ni
defining formulation dp "$p \equiv mv$"^^La Te X ep
in defining formulation dp "$m$, Mass"^^La Te X ep
in defining formulation dp "$p$, Classical Momentum"^^La Te X ep
in defining formulation dp "$v$, Classical Velocity"^^La Te X ep
description ap "momentum(a) of point particle(s) in classical mechanics"@en
wikidata I D ap Q41273 ep

Classical Newton Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalNewtonEquation

when a body is acted upon by a force, the time rate of change of its momentum equals the force
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Classical Dynamics Model ni
contains quantity op Classical Force ni
contains quantity op Classical Position ni
contains quantity op Mass ni
contains quantity op Time ni
generalized by formulation op Classical Hamilton Equations ni
defining formulation dp "$\frac{\mathrm{d^2}}{\mathrm{d}t^2} \vec{q} = \vec{F} / m$"^^La Te X ep
in defining formulation dp "$F$, Classical Force"^^La Te X ep
in defining formulation dp "$m$, Mass"^^La Te X ep
in defining formulation dp "$q$, Classical Position"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is space-continuous dp "true"^^boolean
is time-continuous dp "true"^^boolean
wikidata I D ap Q2397319 ep

Classical Newton Equation (Stoermer Verlet)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalNewtonEquationStoermerVerlet

Originally discovered already by Newton: Essentially a symmetric (and symplectic!) combination of Euler forward and backward methods
belongs to
Mathematical Formulation c
has facts
contains formulation op Euler Backward Method ni
contains formulation op Euler Forward Method ni
contains quantity op Classical Force ni
contains quantity op Classical Position ni
contains quantity op Mass ni
contains quantity op Time ni
contains quantity op Time Step ni
discretizes formulation op Classical Newton Equation ni
similar to formulation op Schrödinger Equation (Second Order Differencing) ni
defining formulation dp "$q(t+\tau)=2q(t)-q(t-\tau)+\tau^2F(q(t))/M$"^^La Te X ep
in defining formulation dp "$F$, Classical Forces"^^La Te X ep
in defining formulation dp "$\tau$, Time Step"^^La Te X ep
in defining formulation dp "$m$, Mass"^^La Te X ep
in defining formulation dp "$q$, Classical Position"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is time-continuous dp "false"^^boolean
description ap "sympletic, reversible time-discretization of Newton's equations of motion"@en
doi I D ap Phys Rev.159.98 ep
wikidata I D ap Q5475314 ep

Classical Positionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalPosition

belongs to
Quantity c
has facts
contained in formulation op Classical Hamilton Equations ni
contained in formulation op Classical Newton Equation ni
generalized by quantity op Length ni
description ap "position of a point particle in classical mechanics"@en

Classical Velocityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClassicalVelocity

belongs to
Quantity c
has facts
generalized by quantity op Velocity ni
description ap "velocity of a point particle in classical mechanics"@en

Closed System Approximationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ClosedSystemApproximation

Note that dissipation as well as dephasing (or more formally: the corresponding rates in the Lindblad equation) are neglected.
belongs to
Mathematical Formulation c
has facts
contained as assumption in op Quantum Liouville Equation ni
contained as assumption in op Schrödinger Equation (Time Dependent) ni
contained as assumption in op Schrödinger Equation (Time Independent) ni
contains quantity op Quantum Damping Rate ni
defining formulation dp "$\gamma \rightarrow 0$"^^La Te X ep
in defining formulation dp "$\gamma$, Quantum Damping Rate"^^La Te X ep
description ap "assuming that a quantum system does not interact with its environment"@en
wikidata I D ap Q4476520 ep

Coefficient Scaling Infectious To Exposedni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#CoefficientScalingInfectiousToExposed

Used in the PDE SEIR Model.
belongs to
Quantity c
has facts
description ap "coefficient scales the number of infectious to estimate the number of exposed individuals"@en

Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#CompetitiveInhibitionConstantUniUniReactionReversibleInhibition

belongs to
Quantity c
has facts
generalized by quantity op Concentration ni
is dimensionless dp "false"^^boolean
description ap "constant for the competitive inhibition in an uni uni reaction"@en

Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#CompetitiveInhibitionConstantUniUniReactionReversibleInhibitionDefinition

Definition of the Competitive Inhibition Constant in an Uni Uni Reaction with a reversible Inhibition
belongs to
Mathematical Formulation c
has facts
contains quantity op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains quantity op Reaction Rate Constant ni
defines op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
defining formulation dp "$K_{ic} \equiv \frac{k_{-3}}{k_3}$"^^La Te X ep
in defining formulation dp "$K_{ic}$, Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$k_3$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean

Complex Number (Dimensionless)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ComplexDimensionless

belongs to
Quantity Kind c
has facts
is dimensionless dp "true"^^boolean
wikidata I D ap Q11567 ep

Complexed Enzyme Concentrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ComplexedEnzymeConcentration

belongs to
Quantity c
has facts
generalized by quantity op Concentration ni
generalized by quantity op Enzyme Concentration ni
description ap "amount of enzyme that is bound to its substrate, product, or intermediates in a reaction environment"@en

Computational Social Scienceni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ComputationalSocialScience

belongs to
Research Field c
has facts
description ap "academic sub-discipline concerned with computational approaches to the social sciences"@en
wikidata I D ap "https://www.wikidata.org/wiki/Q16909867"

Concentrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Concentration

Abundance of a constituent divided by the total volume of a mixture
belongs to
Quantity Kind c
has facts
qudt I D ap Amount Of Substance Concentration.html ep
wikidata I D ap Q3686031 ep

Condition For Positive Solutions In The Multi-Population SI Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ConditionForPositiveSolutionsInTheMultiPopulationSIModel

belongs to
Mathematical Formulation c
has facts
contained as constraint condition in op Multi-Population Discrete Susceptible Infectious Model ni
contains quantity op Contact Rate Between Two Groups ni
contains quantity op Time Step ni
contains quantity op Total Population Size ni
defining formulation dp "$max_i\{\textstyle\sum_{k=1}^K\alpha_{ik}\Delta t N^k/N^i \} \leq 1$"^^La Te X ep
in defining formulation dp "$N^i$, Total Population Size"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha_{ik}$, Contact Rate Between Two Groups"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Condition For Positive Solutions In The Multi-Population SIR Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ConditionForPositiveSolutionsInTheMultiPopulationSIRModel

belongs to
Mathematical Formulation c
has facts
contained as constraint condition in op Multi-Population Discrete Susceptible Infectious Removed Model ni
contains quantity op Contact Rate Between Two Groups ni
contains quantity op Relative Removal Rate ni
contains quantity op Time Step ni
contains quantity op Total Population Size ni
defining formulation dp "$max_i\{\textstyle\sum_{k=1}^K\alpha_{ik}\Delta t N^k/N^i, \gamma_i \Delta t \} \leq 1$"^^La Te X ep
in defining formulation dp "$N^i$, Total Population Size"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha_{ik}$, Contact Rate Between Two Groups"^^La Te X ep
in defining formulation dp "$\gamma_i$, Relative Removal Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Condition For Positive Solutions In The Multi-Population SIS Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ConditionForPositiveSolutionsInTheMultiPopulationSISModel

belongs to
Mathematical Formulation c
has facts
contained as constraint condition in op Multi-Population Discrete Susceptible Infectious Susceptible Model ni
contains formulation op Between Population Contact Rate Equation ni
contains quantity op Between Population Contact Rate ni
contains quantity op Relative Removal Rate ni
contains quantity op Time Step ni
defining formulation dp "$\max_{i} \{a_i, \gamma_i \Delta t\} \leq 1$"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\gamma_i$, Relative Removal rate"^^La Te X ep
in defining formulation dp "$a_i$, Between Population Contact Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Condition For Positive Solutions In The SIR Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ConditionForPositiveSolutionsInTheSIRModel

The time step must be less than the average time required for a successful contact and less than the average infectious period.
belongs to
Mathematical Formulation c
has facts
contained as constraint condition in op Discrete Susceptible Infectious Removed Model ni
contains quantity op Contact Rate ni
contains quantity op Relative Removal Rate ni
contains quantity op Time Step ni
defining formulation dp "$max\{\gamma \Delta t, \alpha \Delta t \} \leq 1$"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha$, Contact Rate"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Condition For Positive Solutions In The SIR Model with Births and Deathsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ConditionForPositiveSolutionsInTheSIRModelWithBirthsAndDeaths

belongs to
Mathematical Formulation c
has facts
contained as constraint condition in op Susceptible Infectious Removed Model with Births and Deaths ni
contains quantity op Birth Rate ni
contains quantity op Relative Removal Rate ni
contains quantity op Time Step ni
defining formulation dp "$(\gamma +\beta) \Delta t \leq 1$"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\beta$, Birth Rate"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Condition For Positive Solutions In The SIS Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ConditionForPositiveSolutionsInTheSISModel

belongs to
Mathematical Formulation c
has facts
contained as constraint condition in op Discrete Susceptible Infectious Susceptible Model ni
contains quantity op Relative Removal Rate ni
contains quantity op Time Step ni
defining formulation dp "$\gamma \Delta t \leq 1$"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
is time-continuous dp "false"^^boolean

Condition For Positive Solutions In The SIS Model with Births and Deathsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ConditionForPositiveSolutionsInTheSISModelWithBirthsAndDeaths

belongs to
Mathematical Formulation c
has facts
contained as constraint condition in op Susceptible Infectious Susceptible Model with Births and Deaths ni
contains quantity op Birth Rate ni
contains quantity op Relative Removal Rate ni
contains quantity op Time Step ni
defining formulation dp "$(\gamma + \beta) \Delta t \leq 1$"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\beta$, Birth Rate"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Condition To Keep Susceptibles Positiveni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ConditionToKeepSusceptiblesPositive

necessary and sufficient condition to ensure that S_n, is positive for all initial conditions (and I_n < N). Implies that the time step At must be less than the average time required for a successful contact.
belongs to
Mathematical Formulation c
has facts
contained as constraint condition in op Discrete Susceptible Infectious Model ni
contains quantity op Contact Rate ni
contains quantity op Time Step ni
defining formulation dp "$\alpha \Delta t \leq 1$"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha$, Contact Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is time-continuous dp "false"^^boolean

Conservation Lawni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ConservationLaw

belongs to
Mathematical Formulation c
has facts
description ap "scientific law regarding conservation of a physical property"@en
wikidata I D ap Q205805 ep

Conservation of City Numbersni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ConservationOfCityNumbers

conservation of city numbers in every region m
belongs to
Mathematical Formulation c
has facts
contains quantity op Number of Cities ni
contains quantity op Number Of Infected Cities ni
contains quantity op Number Of Susceptible Cities ni
contains quantity op Time ni
generalized by formulation op Conservation Law ni
defining formulation dp "$i_m(t) &= P_m - s_m(t)$"^^La Te X ep
in defining formulation dp "$P_m$, Number of Cities"^^La Te X ep
in defining formulation dp "$i_m(t)$, Number Of Infected Cities"^^La Te X ep
in defining formulation dp "$s_m(t)$, Number Of Susceptible Cities"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean
is dynamic dp "true"^^boolean

Constant Population Sizeni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ConstantPopulationSize

Total population size remains constant.
belongs to
Mathematical Formulation c
has facts
contained as constraint condition in op Discrete Susceptible Infectious Model ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Total Population Size ni
generalized by formulation op Conservation Law ni
defining formulation dp "$S_n + I_n \approx N, n = 1,2,...$"^^La Te X ep
in defining formulation dp "$I_n$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_n$, Number Of Susceptible Individuals"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean
is time-continuous dp "false"^^boolean

Contact Networkni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContactNetwork

belongs to
Quantity c
has facts
defined by op Contact Network (Definition) ni
is dimensionless dp "true"^^boolean
description ap "contact network for regions m and n"@en

Contact Network (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContactNetworkDefinition

Definition of contact network for regions m and n.
belongs to
Mathematical Formulation c
has facts
contains quantity op Contact Network ni
contains quantity op Number of Cities ni
contains quantity op Region ni
contains quantity op Region Connectivity ni
defining formulation dp "$G_{m,n} \equiv \begin{cases} \frac{W_{m,n}}{P_m} + \frac{W_{n,m}}{P_n} \quad &\text{for} \quad m \neq n \\ \frac{W_{m,m}}{P_m} \quad &\text{for} \quad m = n \end{cases}$"^^La Te X ep
in defining formulation dp "$G$, Contact Network"^^La Te X ep
in defining formulation dp "$P$, Number of Cities"^^La Te X ep
in defining formulation dp "$W$, Region Connectivity"^^La Te X ep
in defining formulation dp "$m$, Region"^^La Te X ep
in defining formulation dp "$n$, Region"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean
is dynamic dp "false"^^boolean

Contact Network (Time-dependent)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TimeDependentContactNetwork

belongs to
Quantity c
has facts
defined by op Contact Network (Time-dependent, Definition) ni
is dimensionless dp "true"^^boolean
description ap "tuple of spreading rate and contact network interpreted as time-evolving contact network"@en

Contact Network (Time-dependent, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TimeDependentContactNetworkDefinition

definition of tuple of spreading rate and contact network interpreted as time-evolving contact network
belongs to
Mathematical Formulation c
has facts
contains quantity op Contact Network ni
contains quantity op Spreading Rate (Time-dependent) ni
contains quantity op Time ni
contains quantity op Contact Network (Time-dependent) ni
defining formulation dp "$\sigma \equiv (G,\alpha)$"^^La Te X ep
in defining formulation dp "$G$, Contact Network"^^La Te X ep
in defining formulation dp "$\alpha$, Spreading Rate (Time-dependent)"^^La Te X ep
in defining formulation dp "$\sigma$, Contact Network (Time-dependent)"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean
is dynamic dp "true"^^boolean

Contact Network Constraintni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContactNetworkConstraint

constraints applying to contact network
belongs to
Mathematical Formulation c
has facts
contains quantity op Contact Network ni
contains quantity op Region ni
defining formulation dp "$\forall \, m\ne n,\, 0\le G_{m,n} \le 2, \text { and } 0\le G_{m,m} \le 1$"^^La Te X ep
in defining formulation dp "$G$, Contact Network"
in defining formulation dp "$m$, Region"^^La Te X ep
in defining formulation dp "$n$, Region"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean
is dynamic dp "false"^^boolean

Contact Rateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContactRate

Subscript i denotes the ith subpopulation. if no i is provided, then it is a single-population model.
belongs to
Quantity c
has facts
generalized by quantity op Rate ni
is dimensionless dp "false"^^boolean
description ap "average number of individuals with whom an infectious individual makes sufficient contact (to pass infection) during a unit time"@en

Contact Rate Between Two Groupsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContactRateBetweenTwoGroups

belongs to
Quantity c
has facts
description ap "average number of contacts per unit time of an infective in group k with individuals in group i"@en

Continuity Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContinuityEquation

belongs to
Mathematical Formulation c
has facts
contains quantity op Particle Flux Density ni
contains quantity op Particle Number Density ni
generalized by formulation op Conservation Law ni
generalizes formulation op Continuity Equation For Electrons ni
generalizes formulation op Continuity Equation For Holes ni
defining formulation dp "$ {\delta \rho / \delta t} + \nabla \cdot j = 0$"^^La Te X ep
in defining formulation dp "$\rho$, Particle Number Density"^^La Te X ep
in defining formulation dp "$j$, Particle Flux Density"^^La Te X ep
description ap "equation constraining a quantity to flow only via adjacent locations; can express a locality principle"@en
wikidata I D ap Q217219 ep

Continuity Equation For Electronsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContinuityEquationForElectrons

belongs to
Mathematical Formulation c
has facts
contains quantity op Current Density Of Electrons ni
contains quantity op Electric Potential ni
contains quantity op Elementary Charge ni
contains quantity op Fermi Potential For Electrons ni
contains quantity op Fermi Potential For Holes ni
contains quantity op Flux Of Electrons ni
contains quantity op Recombination Of Electron Hole Pairs ni
generalized by formulation op Continuity Equation ni
defining formulation dp "$\nabla \cdot j_n=qR(\psi,\phi_n,\phi_p)$"^^La Te X ep
in defining formulation dp "$R$, Recombination Of Electron Hole Pairs"^^La Te X ep
in defining formulation dp "$\phi_n$, Fermi Potential For Electrons"^^La Te X ep
in defining formulation dp "$\phi_p$, Fermi Potential For Holes"^^La Te X ep
in defining formulation dp "$\psi$, Electric Potential"^^La Te X ep
in defining formulation dp "$j_n$, Current Density Of Electrons"^^La Te X ep
in defining formulation dp "$q$, Elementary Charge"^^La Te X ep
is dynamic dp "false"^^boolean
is space-continuous dp "true"^^boolean
description ap "continuity equation for electrons; for use in semiconductor physics"@en

Continuity Equation For Electrons (Finite Volume)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContinuityEquationForElectronsFiniteVolume

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Scharfetter-Gummel Scheme ni
contains quantity op Control Volume ni
discretizes formulation op Continuity Equation For Electrons ni
defining formulation dp "$j_{n;k,k+1}-j_{n;k-1,k}=qR(\psi_k,\phi_{n;k},\phi_{p;k})|\omega_k|$"^^La Te X ep
in defining formulation dp "$\omega_k$, Control Volume"^^La Te X ep
is space-continuous dp "false"^^boolean
description ap "used within the Scharfetter-Gummel finite volume disretization scheme which is the standard numerical method for solving the van Roosbroeck system"@en

Continuity Equation For Holesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContinuityEquationForHoles

belongs to
Mathematical Formulation c
has facts
contains quantity op Current Density Of Holes ni
contains quantity op Electric Potential ni
contains quantity op Elementary Charge ni
contains quantity op Fermi Potential For Electrons ni
contains quantity op Fermi Potential For Holes ni
contains quantity op Flux Of Holes ni
contains quantity op Recombination Of Electron Hole Pairs ni
generalized by formulation op Continuity Equation ni
defining formulation dp "$\nabla \cdot j_p=-qR(\psi,\phi_n,\phi_p)$"^^La Te X ep
in defining formulation dp "$R$, Recombination of Electron Hole Pairs"^^La Te X ep
in defining formulation dp "$\phi_n$, Fermi Potential For Electrons"^^La Te X ep
in defining formulation dp "$\phi_p$, Fermi Potential For Holes"^^La Te X ep
in defining formulation dp "$\psi$, Electric Potential"^^La Te X ep
in defining formulation dp "$j_p$, Current Density Of Holes"^^La Te X ep
in defining formulation dp "$q$, Elementary Charge"^^La Te X ep
is dynamic dp "false"^^boolean
is space-continuous dp "true"^^boolean
description ap "continuity equation for holes; for use in semiconductor physics"@en

Continuity Equation For Holes (Finite Volume)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContinuityEquationForHolesFiniteVolume

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Scharfetter-Gummel Scheme ni
contains quantity op Control Volume ni
discretizes formulation op Continuity Equation For Holes ni
defining formulation dp "$j_{p;k,k+1}-j_{p;k-1,k}=-qR(\psi_k,\phi_{n;k},\phi_{p;k})|\omega_k|$"^^La Te X ep
in defining formulation dp "$\omega_k$, Control Volume"^^La Te X ep
is space-continuous dp "false"^^boolean
description ap "used within the Scharfetter-Gummel finite volume disretization scheme which is the standard numerical method for solving the van Roosbroeck system"@en

Continuity of the Normal Mass Fluxni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContinuityOfTheNormalMassFlux

belongs to
Mathematical Formulation c
has facts
contains quantity op Fluid Velocity (Free Flow) ni
contains quantity op Fluid Velocity (Porous Medium) ni
contains quantity op Unit Normal Vector ni
defining formulation dp "$[v \cdot n]^{pm} = -[v \cdot n]^{ff} \quad \mathrm{on} \quad \Gamma$"^^La Te X ep
in defining formulation dp "$n$, Normal Unit Vector"^^La Te X ep
in defining formulation dp "$v^{ff}$, Fluid Velocity (Free Flow)"^^La Te X ep
in defining formulation dp "$v^{pm}$, Fluid Velocity (Porous Medium)"^^La Te X ep
description ap "continuity condition to be used as boundary condition within Stokes Darcy hybrid models"@en

Continuity of the Normal Stressesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContinuityOfTheNormalStresses

belongs to
Mathematical Formulation c
has facts
contains quantity op Fluid Pressure (Free Flow) ni
contains quantity op Fluid Pressure (Porous Medium) ni
contains quantity op Fluid Viscous Stress ni
contains quantity op Unit Normal Vector ni
defining formulation dp "$n \cdot [(p I-\tau)n]^{ff} = [p]^{pm} \quad \mathrm{on} \quad \Gamma$"^^La Te X ep
in defining formulation dp "$\tau$, Fluid Viscous Stress"^^La Te X ep
in defining formulation dp "$n$, Unit Normal Vector"^^La Te X ep
in defining formulation dp "$p^{ff}$, Fluid Pressure (Free Flow)"^^La Te X ep
in defining formulation dp "$p^{pm}$, Fluid Pressure (Porous Medium)"^^La Te X ep
description ap "continuity condition to be used as boundary condition within Stokes Darcy hybrid models"@en

Continuous Rate of Change of Infectious in the SI Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContinuousRateOfChangeOfInfectiousInTheSIModel

Rate of Change of Infectious Individuals in the continuous-time SI Model
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Continuous Susceptible Infectious Model ni
contains quantity op Contact Rate ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time ni
contains quantity op Total Population Size ni
discretized by formulation op Susceptibles At Time Step n+1 in The SI Model ni
defining formulation dp "$\frac{d I}{d t}=\frac{\alpha}{N} S I$"^^La Te X ep
in defining formulation dp "$I$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population SIze"^^La Te X ep
in defining formulation dp "$S$, Number Of Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\alpha$, Contact Rate"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "true"^^boolean

Continuous Rate of Change of Infectious in the SIR Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContinuousRateOfChangeOfInfectiousInTheSIRModel

Continuous Rate of Change of Infectious in the SIR Model
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Continuous Susceptible Infectious Removed Model ni
contains quantity op Contact Rate ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Relative Removal Rate ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time ni
contains quantity op Total Population Size ni
defining formulation dp "$\frac{d I}{d t} = I \left( \frac{\alpha}{N} S - \gamma \right)$"^^La Te X ep
in defining formulation dp "$I$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$S$, Number Of Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\alpha$,Contact Rate"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "true"^^boolean

Continuous Rate of change of Infectious in the SIS Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContinuousRateOfChangeOfInfectiousInTheSISModel

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Continuous Susceptible Infectious Susceptible Model ni
contains quantity op Contact Rate ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Relative Removal Rate ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time ni
contains quantity op Total Population Size ni
defining formulation dp "$\frac{d I}{d t} = I \left( \frac{\alpha}{N} S - \gamma \right)$"^^La Te X ep
in defining formulation dp "$I$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$S$, Number Of Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\alpha$, Contact Rate"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "true"^^boolean

Continuous Rate of Change of Removed in the SIR Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContinuousRateOfChangeOfRemovedInTheSIRModel

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Continuous Susceptible Infectious Removed Model ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Relative Removal Rate ni
contains quantity op Number Of Removed Individuals ni
contains quantity op Time ni
defining formulation dp "$\frac{d R}{d t} = R + \gamma I$"^^La Te X ep
in defining formulation dp "$I$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$R$, Number Of Removed Individuals"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "true"^^boolean

Continuous Rate of Change of Susceptibles in the SI Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContinuousRateOfChangeOfSusceptiblesInTheSIModel

Rate of change of S with time in the continuous SI Model
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Continuous Susceptible Infectious Model ni
contains quantity op Contact Rate ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time ni
contains quantity op Total Population Size ni
discretized by formulation op Infectious At Time Step n+1 in the SI Model ni
defining formulation dp "$\frac{d S}{d t} = -\frac{\alpha}{N} S I$"^^La Te X ep
in defining formulation dp "$I$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population SIze"^^La Te X ep
in defining formulation dp "$S$, Number Of Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\alpha$, Contact Rate"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "true"^^boolean

Continuous Rate of change of Susceptibles in the SIR Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContinuousRateOfChangeOfSusceptiblesInTheSIRModel

Continuous Rate of change of S with time in the SIR Model
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Continuous Susceptible Infectious Removed Model ni
contains quantity op Contact Rate ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time ni
contains quantity op Total Population Size ni
defining formulation dp "$\frac{d S}{d t} = -\frac{\alpha}{N} S I $"^^La Te X ep
in defining formulation dp "$I$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$S$, Number Of Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\alpha$, Contact Rate"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "true"^^boolean

Continuous Rate of change of Susceptibles in the SIS Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContinuousRateOfChangeOfSusceptiblesInTheSISModel

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Continuous Susceptible Infectious Susceptible Model ni
contains quantity op Contact Rate ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Relative Removal Rate ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time ni
contains quantity op Total Population Size ni
defining formulation dp "$\frac{d S}{d t} = -\frac{\alpha}{N} S I + \gamma I$"^^La Te X ep
in defining formulation dp "$I$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$S$, Number Of Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\alpha$, Contact Rate"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "true"^^boolean

Continuous Susceptible Infectious Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContinuousSusceptibleInfectiousModel

belongs to
Mathematical Model c
has facts
discretized by model op Discrete Susceptible Infectious Model ni
models op Spreading of Infectious Diseases ni
is deterministic dp "true"^^boolean
is time-continuous dp "true"^^boolean
description ap "continuous-time model for the spreading of infectious diseases considering susceptible and infectious individuals"@en

Continuous Susceptible Infectious Removed Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContinuousSusceptibleInfectiousRemovedModel

belongs to
Mathematical Model c
has facts
discretized by model op Discrete Susceptible Infectious Removed Model ni
generalizes op Continuous Susceptible Infectious Model ni
models op Spreading of Infectious Diseases ni
is deterministic dp "true"^^boolean
is time-continuous dp "true"^^boolean
description ap "continuous-time model for the spreading of infectious diseases considering susceptible, infectious and recovered/removed individuals"@en
wikidata I D ap "https://www.wikidata.org/wiki/Q2206263"

Continuous Susceptible Infectious Susceptible Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContinuousSusceptibleInfectiousSusceptibleModel

belongs to
Mathematical Model c
has facts
discretized by op Discrete Susceptible Infectious Susceptible Model ni
models op Spreading of Infectious Diseases ni
is deterministic dp "true"^^boolean
is time-continuous dp "true"^^boolean
description ap "continuous-time model for the spreading of infectious diseases with temporary resistance considering susceptible and infectious individuals"@en
wikidata I D ap "https://www.wikidata.org/wiki/Q2351772"

Continuum Mechanicsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ContinuumMechanics

belongs to
Research Field c
has facts
contains problem op Flow in porous media ni
contains problem op Free flow coupled to porous media flow ni
contains problem op Free flow of an incompressible fluid ni
description ap "branch of mechanics that deals with the analysis of the kinematics and the mechanical behavior of materials modeled as a continuous mass"@en
wikidata I D ap Q193463 ep

Control System Durationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemDuration

belongs to
Quantity c
has facts
description ap "time after which a (optimal) control should have reached the target"@en

Control System Initialni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemInitial

belongs to
Quantity c
has facts
description ap "initial value for the state vector of a control system"@en

Control System Initial (Reduced)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemInitialReduced

belongs to
Mathematical Formulation c
has facts
contains initial condition op Initial Control State ni
contains quantity op MOR Transformation Matrix ni
defining formulation dp "$\tilde{x}_0=T^{-1}x_0$"^^La Te X ep
in defining formulation dp "$T$, MOR Transformation Matrix"^^La Te X ep
in defining formulation dp "$x_0$, Initial Control State"^^La Te X ep
description ap "initial value for the state vector of a control system; after model order reduction"@en

Control System Inputni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemInput

belongs to
Quantity c
has facts
description ap "input to a control system"@en

Control System Input Bilinearni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemInputBilinear

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Control System Model (Bilinear) ni
contains quantity op Control System Input ni
contains quantity op Control System Matrix A ni
contains quantity op Control System Matrix B ni
contains quantity op Control System Matrix N ni
contains quantity op Control System State ni
contains quantity op Time ni
generalizes formulation op Control System Input Linear ni
generalizes formulation op Quantum Lindblad Equation ni
generalizes formulation op Quantum Liouville Equation ni
generalizes formulation op Schrödinger Equation (Time Dependent) ni
defining formulation dp "$\dot{x}(t)=(A+u(t)N)x(t)+Bu(t)$"^^La Te X ep
in defining formulation dp "$A$, Control System Matrix A"^^La Te X ep
in defining formulation dp "$B$, Control System Matrix B"^^La Te X ep
in defining formulation dp "$N$, Control System Matrix N"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$u$, Control System Input"^^La Te X ep
in defining formulation dp "$x$, Control System State"^^La Te X ep
description ap "bilinear input equation for control systems"@en

Control System Input Bilinear (Reduced)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemInputBilinearReduced

belongs to
Mathematical Formulation c
has facts
approximates formulation op Control System Input Bilinear ni
contains quantity op Control System Input ni
contains quantity op Control System Matrix A (Reduced) ni
contains quantity op Control System Matrix B (Reduced) ni
contains quantity op Control System Matrix N (Reduced) ni
contains quantity op Control System State (Reduced) ni
contains quantity op Time ni
generalizes formulation op Control System Input Linear (Reduced) ni
defining formulation dp "$\dot{\tilde{x}}(t)=(\tilde{A}+u(t)\tilde{N})\tilde{x}(t)+\tilde{B}u(t)$"^^La Te X ep
in defining formulation dp "$\tilde{A}$, Control System Matrix A (Reduced)"^^La Te X ep
in defining formulation dp "$\tilde{B}$, Control System Matrix B (Reduced)"^^La Te X ep
in defining formulation dp "$\tilde{N}$, Control System Matrix N (Reduced)"^^La Te X ep
in defining formulation dp "$\tilde{x}$, Control System State (Reduced)"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$u$, Control System Input"^^La Te X ep
description ap "bilinear input equation for control systems; after model order reduction"@en

Control System Input Linearni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemInputLinear

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Control System Model (Linear) ni
contains quantity op Control System Input ni
contains quantity op Control System Matrix A ni
contains quantity op Control System Matrix B ni
contains quantity op Control System State ni
contains quantity op Time ni
generalizes formulation op Quantum Lindblad Equation ni
generalizes formulation op Quantum Liouville Equation ni
generalizes formulation op Schrödinger Equation (Time Dependent) ni
defining formulation dp "$\dot{x}(t)=Ax(t)+Bu(t)$"^^La Te X ep
in defining formulation dp "$A$, Control System Matrix A"^^La Te X ep
in defining formulation dp "$B$, Control System Matrix B"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$u$, Control System Input"^^La Te X ep
in defining formulation dp "$x$, Control System State"^^La Te X ep
description ap "linear input equation for control systems"@en

Control System Input Linear (Reduced)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemInputLinearReduced

belongs to
Mathematical Formulation c
has facts
approximates formulation op Control System Input Linear ni
contains quantity op Control System Input ni
contains quantity op Control System Matrix A (Reduced) ni
contains quantity op Control System Matrix B (Reduced) ni
contains quantity op Control System State (Reduced) ni
contains quantity op Time ni
defining formulation dp "$\dot{\tilde{x}}(t)=\tilde{A}\tilde{x}(t)+\tilde{B}u(t)$"^^La Te X ep
in defining formulation dp "$\tilde{A}$, Control System Matrix A (Reduced)"^^La Te X ep
in defining formulation dp "$\tilde{B}$, Control System Matrix B (Reduced)"^^La Te X ep
in defining formulation dp "$\tilde{x}$, Control System State (Reduced)"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$u$, Control System Input"^^La Te X ep
description ap "linear input equation for control systems; after model order reduction"@en

Control System Lagrange Multiplierni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemLagrangeMultiplier

belongs to
Quantity c
has facts
description ap "method to solve constrained optimization problems for control systems"@en

Control System Matrix Ani back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemMatrixA

belongs to
Quantity c
has facts
description ap "homogeneous part of (linear) input equation for control systems"@en

Control System Matrix A (Reduced)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemMatrixAReduced

belongs to
Quantity c
has facts
defined by op Control System Matrix A (Reduced, Definition) ni
description ap "homogeneous part of (linear) input equation for control systems; after model order reduction"@en

Control System Matrix A (Reduced, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemMatrixAReducedDefinition

belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Matrix A ni
contains quantity op Control System Matrix A (Reduced) ni
contains quantity op MOR Transformation Matrix ni
defines op Control System Matrix A (Reduced) ni
defining formulation dp "$\tilde{A} \equiv T^{-1}AT$"^^La Te X ep
in defining formulation dp "$A$, Control System Matrix A"^^La Te X ep
in defining formulation dp "$T$, MOR Transformation Matrix"^^La Te X ep
in defining formulation dp "$\tilde{A}$, Control System Matrix A (Reduced)"^^La Te X ep
description ap "homogeneous part of (linear) input equation for control systems; after model order reduction"@en

Control System Matrix Bni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemMatrixB

belongs to
Quantity c
has facts
description ap "inhomogeneous part of (linear) input equation for control systems"@en

Control System Matrix B (Reduced)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemMatrixBReduced

belongs to
Quantity c
has facts
defined by op Control System Matrix B (Reduced, Definition) ni
description ap "inhomogeneous part of (linear) input equation for control systems; after model order reduction"@en

Control System Matrix B (Reduced, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemMatrixBReducedDefinition

belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Matrix B ni
contains quantity op Control System Matrix B (Reduced) ni
contains quantity op MOR Transformation Matrix ni
defines op Control System Matrix B (Reduced) ni
defining formulation dp "$\tilde{B} \equiv T^{-1}BT$"^^La Te X ep
in defining formulation dp "$B$, Control System Matrix B"^^La Te X ep
in defining formulation dp "$T$, MOR Transformation Matrix"^^La Te X ep
in defining formulation dp "$\tilde{B}$, Control System Matrix B (Reduced)"^^La Te X ep
description ap "inhomogeneous part of (linear) input equation for control systems; after model order reduction"@en

Control System Matrix Cni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemMatrixC

belongs to
Quantity c
has facts
description ap "linear part of output equation for control systems"@en

Control System Matrix C (Reduced)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemMatrixCReduced

belongs to
Quantity c
has facts
contained in formulation op Control System Output Linear (Reduced) ni
defined by op Control System Matrix C (Reduced, Definition) ni
description ap "linear part of output equation for control systems; after model order reduction"@en

Control System Matrix C (Reduced, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemMatrixCReducedDefinition

belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Matrix C ni
contains quantity op Control System Matrix C (Reduced) ni
contains quantity op MOR Transformation Matrix ni
defines op Control System Matrix C (Reduced) ni
defining formulation dp "$\tilde{C} \equiv CT$"^^La Te X ep
in defining formulation dp "$C$, Control System Matrix C"^^La Te X ep
in defining formulation dp "$T$, MOR Transformation Matrix"^^La Te X ep
in defining formulation dp "$\tilde{C}$, Control System Matrix C (Reduced)"^^La Te X ep
description ap "linear part of output equation for control systems; after model order reduction"@en

Control System Matrix Dni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemMatrixD

belongs to
Quantity c
has facts
description ap "quadratic part of output equation for control systems"@en

Control System Matrix D (Reduced)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemMatrixDReduced

belongs to
Quantity c
has facts
contained in formulation op Control System Output Quadratic (Reduced) ni
defined by op Control System Matrix D (Reduced, Definition) ni
description ap "quadratic part of output equation for control systems; after model order reduction"@en

Control System Matrix D (Reduced, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemMatrixDReducedDefinition

belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Matrix D ni
contains quantity op Control System Matrix D (Reduced) ni
contains quantity op MOR Transformation Matrix ni
defines op Control System Matrix D (Reduced) ni
defining formulation dp "$\tilde{D} \equiv T^{-1}DT$"^^La Te X ep
in defining formulation dp "$D$, Control System Matrix D"^^La Te X ep
in defining formulation dp "$T$, MOR Transformation Matrix"^^La Te X ep
in defining formulation dp "$\tilde{D}$, Control System Matrix D (Reduced)"^^La Te X ep
description ap "quadratic part of output equation for control systems; after model order reduction"@en

Control System Matrix Nni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemMatrixN

belongs to
Quantity c
has facts
description ap "bilinear part of input equation for control systems"@en

Control System Matrix N (Reduced)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemMatrixNReduced

belongs to
Quantity c
has facts
defined by op Control System Matrix N (Reduced, Definition) ni
description ap "bilinear part of input equationfor control systems; after model order reduction"@en

Control System Matrix N (Reduced, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemMatrixNReducedDefinition

belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Matrix N ni
contains quantity op Control System Matrix N (Reduced) ni
contains quantity op MOR Transformation Matrix ni
defines op Control System Matrix N (Reduced) ni
defining formulation dp "$\tilde{N} \equiv T^{-1}NT$"^^La Te X ep
in defining formulation dp "$N$, Control System Matrix N"^^La Te X ep
in defining formulation dp "$T$, MOR Transformation Matrix"^^La Te X ep
in defining formulation dp "$\tilde{N}$, Control System Matrix N (Reduced)"^^La Te X ep
description ap "bilinear part of input equationfor control systems; after model order reduction"@en

Control System Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemModel

In general, there are there are two types of controls: open-loop control (feedforward), and closed-loop control (feedback). In many applications of practical relevance, the state vector x is very high-dimensional, even though input u and output y may be low-dimensional
belongs to
Mathematical Model c
has facts
applied by task op Optimal Control ni
generalizes model op Control System Model (Bilinear) ni
models op Molecular Spectroscopy (Transient) ni
models op Spin Qbit Shuttling ni
description ap "branch of engineering and mathematics that deals with the behavior of dynamical systems with inputs, that modify their behavior"@en
wikidata I D ap Q6501221 ep
wikidata I D ap Q959968 ep

Control System Model (Bilinear)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemModelBilinear

belongs to
Mathematical Model c
has facts
contains initial condition op Initial Control State ni
generalizes model op Control System Model (Linear) ni
models op Molecular Spectroscopy (Transient) ni
models op Spin Qbit Shuttling ni
description ap "control system with bi-linear input equation"@en

Control System Model (Linear)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemModelLinear

belongs to
Mathematical Model c
has facts
description ap "control system with linear input equation"@en

Control System Outputni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemOutput

belongs to
Quantity c
has facts
description ap "output from a control system"@en

Control System Output Linearni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemOutputLinear

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Balanced Truncation (Bi-linear) ni
contained as formulation in op Control System Model (Bilinear) ni
contained as formulation in op Control System Model (Linear) ni
contains quantity op Control System Matrix C ni
contains quantity op Control System Output ni
contains quantity op Control System State ni
contains quantity op Time ni
defining formulation dp "$y(t)=Cx(t)$"^^La Te X ep
in defining formulation dp "$C$, Control System Matrix C"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$x$, Control System State"^^La Te X ep
in defining formulation dp "$y$, Control System Output"^^La Te X ep
description ap "linear output equation for control systems"@en

Control System Output Linear (Reduced)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemOutputLinearReduced

belongs to
Mathematical Formulation c
has facts
approximates formulation op Control System Output Linear ni
contains quantity op Control System Output ni
contains quantity op Time ni
defining formulation dp "$y(t)=\tilde{C}\tilde{x}(t)$"^^La Te X ep
in defining formulation dp "$\tilde{C}$, Control System Matrix C (Reduced)"^^La Te X ep
in defining formulation dp "$\tilde{x}$, Control System State (Reduced)"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$y$, Control System Output"^^La Te X ep
description ap "linear output equation for control systems; after model order reduction"@en

Control System Output Quadraticni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemOutputQuadratic

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Balanced Truncation (Bi-linear) ni
contained as formulation in op Control System Model (Bilinear) ni
contained as formulation in op Control System Model (Linear) ni
contains quantity op Control System Matrix D ni
contains quantity op Control System Output ni
contains quantity op Control System State ni
contains quantity op Time ni
defining formulation dp "$y(t)=x^{\dag}(t)Dx(t)$"^^La Te X ep
in defining formulation dp "$D$, Control System Matrix D"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$x$, Control System State"^^La Te X ep
in defining formulation dp "$y$, Control System Output"^^La Te X ep
description ap "quadratic output equation for control systems"@en

Control System Output Quadratic (Reduced)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemOutputQuadraticReduced

belongs to
Mathematical Formulation c
has facts
approximates formulation op Control System Output Quadratic ni
contains quantity op Control System Output ni
contains quantity op Time ni
defining formulation dp "$y(t)=\tilde{x}^{\dag}(t)\tilde{D}\tilde{x}(t)$"^^La Te X ep
in defining formulation dp "$\tilde{D}$, Control System Matrix D (Reduced)"^^La Te X ep
in defining formulation dp "$\tilde{x}$, Control System State (Reduced)"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$y$, Control System Output"^^La Te X ep
description ap "quadratic output equation for control systems; after model order reduction"@en

Control System Stateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemState

belongs to
Quantity c
has facts
description ap "state vector of a dynamical system for control systems"@en

Control System State (Reduced)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemStateReduced

belongs to
Quantity c
has facts
contained in formulation op Control System Output Linear (Reduced) ni
contained in formulation op Control System Output Quadratic (Reduced) ni
defined by op Control System State (Reduced, Definition) ni
description ap "state vector of a dynamical system for control systems; after model order reduction"@en

Control System State (Reduced, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemStateReducedDefinition

belongs to
Mathematical Formulation c
has facts
contains quantity op Control System State ni
contains quantity op Control System State (Reduced) ni
contains quantity op MOR Transformation Matrix ni
defining formulation dp "$\tilde{x} \equiv T^{-1}x$"^^La Te X ep
in defining formulation dp "$\tilde{x}$, Control System State (Reduced)"
in defining formulation dp "$T$, MOR Transformation Matrix"^^La Te X ep
in defining formulation dp "$x$, Control System State"^^La Te X ep
description ap "state vector of a dynamical system for control systems; after model order reduction"@en

Control System Time Evolutionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemTimeEvolution

belongs to
Computational Task c
has facts
applies model op Control System Model ni
generalizes task op Control System Time Evolution (Bi-linear) ni
description ap "computing the time evolution of a control system, for given initial state and given control , yielding output as a function of time"@en

Control System Time Evolution (Linear)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlSystemTimeEvolutionLinear

belongs to
Computational Task c
has facts
applies model op Control System Model (Linear) ni
contains formulation op Control System Input Linear ni
contains formulation op Control System Output Linear ni
contains initial condition op Initial Control State ni
contains input op Control System Input ni
contains output op Control System Output ni
contains parameter op Control System Matrix A ni
contains parameter op Control System Matrix B ni
contains parameter op Control System Matrix C ni
description ap "computing the time evolution of a control system with linear input equation"@en

Control Volumeni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlVolume

used for example in the Scharfetter-Gummel discretization of the van-Roosbroeck system
belongs to
Quantity c
has facts
contained in formulation op Finite Volume Method ni
defined by op Control Volume (Definition) ni
description ap "mathematical abstraction employed in mathematical models of continuum mechanics and thermodynamics used within finite volume discretizations"@en
wikidata I D ap Q5165895 ep

Control Volume (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ControlVolumeDefinition

belongs to
Mathematical Formulation c
has facts
contains quantity op Control Volume ni
contains quantity op Spatial Variable ni
defining formulation dp "$\omega_k \equiv [x_{k-1,k}-x_{k,k+1}]$"^^La Te X ep
in defining formulation dp "$\omega$, Control Volume"^^La Te X ep
in defining formulation dp "$x$, Spatial Variable"^^La Te X ep
description ap "control volume used within finite volume discretizations, e.g. the Scharfetter-Gummel discretization of the van-Roosbroeck system"@en
wikidata I D ap Q234072 ep

Coriolis Coupling Constantni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#CoriolisCouplingConstant

belongs to
Quantity c
has facts
description ap "description of the interaction between rotational and vibrational motions, e.g., in molecules"@en
doi I D ap Phys Rev.56.680 ep
wikidata I D ap Q7370329 ep

Costsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Costs

belongs to
Quantity Kind c
has facts
wikidata I D ap Q240673 ep

Costs of Line Conceptni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#CostsOfLineConcept

belongs to
Quantity c
has facts
generalized by quantity op Costs ni
description ap "summarized costs of a line concept"@en

Costs per Unitni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#CostsPerUnit

Costs per unit of something, e.g. costs per 1km, costs per vehicle, costs per line, costs per edge,...
belongs to
Quantity c
has facts
generalized by quantity op Costs ni
description ap "costs per unit of something"@en

Coulomb Friction Of Two Particlesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Coulomb_Friction_Of_Two_Particles

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Linear Discrete Element Method ni
defining formulation dp "if $F^{T, cons}_{ij}> \mu F_{ij}^N$ then $\bm F_{ij}^T = \mu F_{ij}^N \bm\xi_{ij}/\lVert \bm\xi_{ij}\rVert$"^^La Te X ep
in defining formulation dp "$F_{ij}^{T, cons}=-k_{ij}^T\lVert \bm \xi_{ij}\rVert$, conservative part of tangential interaction force"^^La Te X ep
description ap "slipping occurs, if tangential force is high in relation to normal force in the contact of two particles"@en

Coupling Currentni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#CouplingCurrent

belongs to
Quantity c
has facts
generalized by quantity op Electric Current ni
description ap "transfer current from one circuit to another"@en

Cross Sectionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#CrossSection

In geometry and in natural sciences, a cross section is the intersection of a body in 3D space with a plane.
belongs to
Quantity c
has facts
generalized by quantity op Area ni
description ap "the intersection of a body in 3D space with a plane"@en
wikidata I D ap Q845080 ep

Cundall (1979) A discrete numerical model for granular assembliesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Cundall_1979_Discrete_model_granular_assemblies

belongs to
Publication c
has facts
doi I D ap geot.1979.29.1.47 ep

Current Densityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#CurrentDensity

The (electric) current density is defined as the amount of charge per unit time that flows through a unit area
belongs to
Quantity c
has facts
generalizes quantity op Current Density Of Electrons ni
generalizes quantity op Current Density Of Holes ni
description ap "amount of charge per unit time that flows through a unit area"@en
wikidata I D ap Q234072 ep

Current Density Of Electronsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#CurrentDensityOfElectrons

belongs to
Quantity c
has facts
defined by op Current Density Of Electrons (Definition) ni
description ap "density of current of the electrons, e.g., in a semiconductor device"@en
alt Label ap "flux of electrons"@en

Current Density Of Electrons (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#CurrentDensityOfElectronsDefinition

belongs to
Mathematical Formulation c
has facts
contains quantity op Current Density Of Electrons ni
contains quantity op Density Of Electrons ni
contains quantity op Electric Potential ni
contains quantity op Elementary Charge ni
contains quantity op Fermi Potential For Electrons ni
contains quantity op Mobility Of Electrons ni
defining formulation dp "$j_n \equiv -q\mu_nn(\psi\phi_n) \nabla \phi_n$"^^La Te X ep
in defining formulation dp "$\mu_n$, Mobility Of Electrons"^^La Te X ep
in defining formulation dp "$\phi_n$, Fermi Potential For Electrons"^^La Te X ep
in defining formulation dp "$\psi$, Electric Potential"^^La Te X ep
in defining formulation dp "$j_n$, Current Density Of Electrons"^^La Te X ep
in defining formulation dp "$n$, Density Of Electrons"^^La Te X ep
in defining formulation dp "$q$, Elementary Charge"^^La Te X ep
is dynamic dp "false"^^boolean
is space-continuous dp "true"^^boolean
description ap "for use in semiconductor physics; also known as flux of electrons"@en
alt Label ap "Flux of Electrons"@en

Current Density Of Holesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#CurrentDensityOfHoles

belongs to
Quantity c
has facts
defined by op Current Density Of Holes (Definition) ni
similar to quantity op Current Density Of Electrons ni
description ap "density of current of the holes, e.g., in a semiconductor device"@en
alt Label ap "flux of holes"@en

Current Density Of Holes (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#CurrentDensityOfHolesDefinition

belongs to
Mathematical Formulation c
has facts
contains quantity op Current Density Of Holes ni
contains quantity op Density Of Holes ni
contains quantity op Electric Potential ni
contains quantity op Elementary Charge ni
contains quantity op Fermi Potential For Holes ni
contains quantity op Mobility Of Holes ni
defining formulation dp "$j_p \equiv -q\mu_pp(\psi\phi_p) \nabla \phi_p$"^^La Te X ep
in defining formulation dp "$\mu_p$, Mobility Of Holes"^^La Te X ep
in defining formulation dp "$\phi_p$, Fermi Potential For Holes"^^La Te X ep
in defining formulation dp "$\psi$, Electric Potential"^^La Te X ep
in defining formulation dp "$j_p$, Current Density Of Holes"^^La Te X ep
in defining formulation dp "$p$, Density Of Holes"^^La Te X ep
in defining formulation dp "$q$, Elementary Charge"^^La Te X ep
is dynamic dp "false"^^boolean
is space-continuous dp "true"^^boolean
description ap "for use in semiconductor physics; also known as flux of holes"@en
alt Label ap "Flux Of Holes"@en

Current flow in semiconductor devicesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#CurrentFlowInSemiconductorDevices

belongs to
Research Problem c
has facts
contained in field op Semiconductor Physics ni
modeled by op van Roosbroeck Model ni
description ap "flow of electrical charge carriers coupled to electrostatic potential distribution in semiconductor devices"@en

Current Procedural Terminologyni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#CurrentProceduralTerminology

belongs to
Quantity c
has facts
description ap "procedure codes"@en
wikidata I D ap Q964984 ep

Darcy Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DarcyEquation

mathematical model describing the flow of a fluid through a porous medium.
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Darcy Model ni
contains quantity op Fluid Dynamic Viscosity (Porous Medium) ni
contains quantity op Fluid Intrinsic Permeability (Porous Medium) ni
contains quantity op Fluid Pressure (Porous Medium) ni
contains quantity op Fluid Velocity (Porous Medium) ni
defining formulation dp "$\begin{align*} v^{pm} = -K \mu^{-1} \nabla p^{vm} \\ \nabla \cdot v^{pm} = 0 \end{align*}$"^^La Te X ep
in defining formulation dp "$K$, Fluid Intrinsic Permeability (Porous Medium)"^^La Te X ep
in defining formulation dp "$\mu$, Fluid Dynamic Viscosity (Porous Medium)"^^La Te X ep
in defining formulation dp "$p^{pm}$, Fluid Pressure (Porous Medium)"^^La Te X ep
in defining formulation dp "$v^{pm}$, Fluid Velocity (Porous Medium)"^^La Te X ep
is space-continuous dp "true"^^boolean
is time-continuous dp "true"^^boolean
description ap "describing the flow of a fluid through a porous medium"@en
wikidata I D ap Q392416 ep

Darcy Equation (Euler Backward)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DarcyEquationEulerBackward

belongs to
Mathematical Formulation c
has facts
discretizes formulation op Darcy Equation ni
is time-continuous dp "false"^^boolean
description ap "discretizing the Darcy equation by a first-oder backward Euler scheme in time"@en

Darcy Equation (Finite Volume)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DarcyEquationFiniteVolume

belongs to
Mathematical Formulation c
has facts
discretizes formulation op Darcy Equation ni
is space-continuous dp "false"^^boolean
description ap "discretizing the Darcy equation by a finite volume scheme in space"@en

Darcy Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DarcyModel

belongs to
Mathematical Model c
has facts
description ap "mathematical model describing the flow of a fluid through a porous medium"@en
wikidata I D ap Q392416 ep

Darcy Model (Discretized)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DarcyModelDiscretized

belongs to
Mathematical Model c
has facts
contains formulation op Darcy Equation (Euler Backward) ni
contains formulation op Darcy Equation (Finite Volume) ni
discretizes model op Darcy Model ni
description ap "discretized version of Darcy's model describing the flow of a fluid through a porous medium"@en

Darwin-Howie-Whelan Equation for a strained crystalni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DarwinHowieWhelanEquationStrained

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Dynamical Electron Scattering Model ni
contains quantity op Unit Normal Vector ni
defining formulation dp "$\begin{align*} \frac{\mathrm d}{\mathrm d z} \varphi_{\mathbf{g}}(z) &= 2\mathrm{i} \pi \Big(s_{\mathbf{g}} + \frac{\mathrm d}{\mathrm d z}(\mathbf{g}\cdot \mathbf{u}(\mathbf{r}))\Big)\varphi_{\mathbf{g}}(z)+ \mathrm{i} \pi\sum_{\mathbf{h}\in \Lambda^*_m} U_{\mathbf{g-h}}\varphi_{\mathbf{h}}(z)\\ \quad s_g &= -\frac{g\cdot(2k_0+g)}{2n\cdot(k_0+g)} \end{align*}$"^^La Te X ep
in defining formulation dp "$U_g$, Electric Potential Fourier Coefficients"^^La Te X ep
in defining formulation dp "$\Lambda^*_m$, Reciprocal Lattice"^^La Te X ep
in defining formulation dp "$\psi_g$, Amplitude of Electron Wave"^^La Te X ep
in defining formulation dp "$g$, Reciprocal Lattice Vectors"^^La Te X ep
in defining formulation dp "$k_0$, Wave Vector of an Electron"^^La Te X ep
in defining formulation dp "$n$, Unit Normal Vector"^^La Te X ep
in defining formulation dp "$s_g$, Excitation Error"^^La Te X ep
in defining formulation dp "$u$, Displacement of Atoms"^^La Te X ep
description ap "simuating TEM images by numerically solving the Darwin–Howie–Whelan equation describing the electron propagation"@en

Darwin-Howie-Whelan Equation for an unstrained crystalni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DarwinHowieWhelanEquationNoStrain

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Dynamical Electron Scattering Model ni
contains quantity op Unit Normal Vector ni
generalized by formulation op Darwin-Howie-Whelan Equation for a strained crystal ni
defining formulation dp "$\begin{align*} \frac{\mathrm d}{\mathrm d z} \psi_\mathbf{g}(z) &= 2\mathrm{i} \pi s_\mathbf{g} \psi_\mathbf{g}(z)+ \frac{\mathrm{i} \pi}{\rho_\mathbf{g}}\sum_{\mathbf{h}\in \Lambda^*_m} U_{\mathbf{g-h}}\psi_\mathbf{h}(z)\\ \quad s_g &= -\frac{g\cdot(2k_0+g)}{2n\cdot(k_0+g)} \end{align*}$"^^La Te X ep
in defining formulation dp "$U_g$, Electric Potential Fourier Coefficients"^^La Te X ep
in defining formulation dp "$\Lambda^*_m$, Reciprocal Lattice"^^La Te X ep
in defining formulation dp "$\psi_g$, Amplitude of Electron Wave"^^La Te X ep
in defining formulation dp "$g$, Reciprocal Lattice Vectors"^^La Te X ep
in defining formulation dp "$k_0$, Wave Vector of an Electron"^^La Te X ep
in defining formulation dp "$n$, Unit Normal Vector"^^La Te X ep
in defining formulation dp "$s_g$, Excitation error"^^La Te X ep
description ap "simuating TEM images of an unstrained crystal by numerically solving the Darwin–Howie–Whelan equation describing the electron propagation"@en

de Broglie Wavelengthni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#deBroglieWavelength

playing a crucial role for the wave-particle duality in quantum mechanics.
belongs to
Quantity c
has facts
defined by op de Broglie Wavelength (Definition) ni
description ap "wavelength of matter waves in quantum mechanics"@en
wikidata I D ap Q100981463 ep

de Broglie Wavelength (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#deBroglieWaveLengthDefinition

belongs to
Mathematical Formulation c
has facts
contains quantity op Classical Momentum ni
contains quantity op Planck Constant ni
contains quantity op de Broglie Wavelength ni
defines op de Broglie Wavelength ni
defining formulation dp "$\lambda \equiv \frac{h}{p}$"^^La Te X ep
in defining formulation dp "$\lambda$, de Broglie Wavelength"^^La Te X ep
in defining formulation dp "$h$, Planck Constant"^^La Te X ep
in defining formulation dp "$p$, Classical Momentum"^^La Te X ep
description ap "wavelength of matter waves, playing a crucial role for the wave-particle duality in quantum mechanics"@en
wikidata I D ap Q100981463 ep

Death Countni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DeathCount

belongs to
Quantity c
has facts
description ap "death count, at a given age"@en

Decision Variableni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DecisionVariable

In case of line pool generation, it decides if a line is included or not
belongs to
Quantity c
has facts
defined by op Decision Variable (Definition) ni
description ap "variable deciding if an object is chosen or not"@en

Decision Variable (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DecisionVariableDefinition

A variable deciding if an object is chosen or not. In case of line pool generation, it decides if a line is included or not
belongs to
Mathematical Formulation c
has facts
contains quantity op Decision Variable ni
defining formulation dp "$x_l \equiv 1$ if $l$ is chosen, otherwise $x_l=0$"^^La Te X ep
in defining formulation dp "$x_l$, Decision Variable"^^La Te X ep

Demographyni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Demography

belongs to
Research Field c
has facts
contains problem op Mortality Modeling ni
description ap "statistical and theoretical study of populations: size, composition, and how they change through fertility, mortality, and migration"@en
mardi I D ap Item: Q116324 ep
wikidata I D ap Q37732 ep

Denoising for Improved Parametric MRI of the Kidneyni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DenoisingForImprovedParametricMRIOfTheKidney

belongs to
Computational Task c
has facts
applies model op Gaussian Noise Model ni
contains formulation op Non-Local Means ni
description ap "denoising for improved parametric MRI (magnetic resonance imaging) of the kidney"@en
doi I D ap 978 1 0716 0978 1 34 ep

Densityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Density

Mass per volume of a substance, aka volumetric mass density or specific mass
belongs to
Quantity Kind c
has facts
qudt I D ap Density ep
wikidata I D ap Q29539 ep

Density Fraction Coefficientni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DensityFractionCoefficient

Coeffieicnts used in the definition of the density fractions in the SEIR Model
belongs to
Quantity c
has facts
description ap "coefficients used in the definition of the density fractions"@en

Density Of Airni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DensityOfAir

belongs to
Quantity c
has facts
generalized by quantity op Density ni
description ap "mass per unit volume of the atmosphere of the planet Earth"@en
wikidata I D ap Q1511415 ep

Density Of Electronsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DensityOfElectrons

For use in semiconductor physics
belongs to
Quantity c
has facts
generalized by quantity op Particle Number Density ni
description ap "probability density of electrons being somewhere"@en
wikidata I D ap Q905186 ep

Density Of Holesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DensityOfHoles

For use in semiconductor physics
belongs to
Quantity c
has facts
contained in formulation op Poisson Equation For The Electric Potential ni
generalized by quantity op Particle Number Density ni
description ap "probability density of holes being somewhere"@en

Density Of States For Conduction Bandni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DensityOfStatesForConductionBand

belongs to
Quantity c
has facts
description ap "number of allowed states per unit energy range for conduction band"@en

Density Of States For Valence Bandni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DensityOfStatesForValenceBand

belongs to
Quantity c
has facts
description ap "number of allowed states per unit energy range for valence band"@en

Detailed Balance Principleni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DetailedBalancePrinciple

The principle of detailed balance can be used in kinetic systems which are decomposed into elementary processes (collisions, or steps, or elementary reactions).
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Quantum Lindblad Equation ni
contains quantity op Boltzmann Constant ni
contains quantity op Quantum Damping Rate ni
contains quantity op Quantum Eigen Energy ni
contains quantity op Quantum Number ni
contains quantity op Temperature ni
defining formulation dp "$\Gamma_{n \to m, m > n} = e^{-\frac{E_m-E_n}{k_BT}} \Gamma_{m \to n, m > n}$"^^La Te X ep
in defining formulation dp "$E$, Quantum Eigen Energy"^^La Te X ep
in defining formulation dp "$T$, Temperature"^^La Te X ep
in defining formulation dp "$\Gamma$, Quantum Damping Rate"^^La Te X ep
in defining formulation dp "$k_B$, Boltzmann constant"^^La Te X ep
in defining formulation dp "$m$, Quantum Number"^^La Te X ep
in defining formulation dp "$n$, Quantum Number"^^La Te X ep
description ap "at thermal equilibrium, each elementary process is in equilibrium with its reverse process"@en
wikidata I D ap Q1201087 ep

Diffusion Coefficientni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DiffusionConstant

Diffusion coefficient is usually written as the proportionality constant between the molar flux due to molecular diffusion and the negative value of the gradient in the concentration of the species.
belongs to
Quantity c
has facts
contained in formulation op Fick Equation ni
description ap "proportionality constant between the molar flux and the negative value of the gradient in the concentration of the species"@en
alt Label ap "Diffusivity"@en
alt Label ap "Mass Diffusivity"@en
wikidata I D ap Q604008 ep

Diffusion Coefficient for SEIR Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DiffusionCoefficient

describes the spatial mixing of the subpopulations and may, in general, depend on the spatial position.
belongs to
Quantity c
has facts
description ap "spatial mixing of the subpopulations"@en

Diffusion Fluxni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DiffusionFlux

belongs to
Quantity c
has facts
contained in formulation op Fick Equation ni
generalized by quantity op Particle Flux Density ni
description ap "solute mass removal rate resulting from diffusion"@en

Diffusion Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DiffusionsModel

belongs to
Mathematical Model c
has facts
contains formulation op Fick Equation ni
generalized by model op Classical Fokker Planck Model ni
description ap "mathematical model describing transport of mass|particles by diffusion"@en

Dirac Delta Distributionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DiracDeltaDistribution

Value is zero everywhere except at zero, and whose integral over the entire real line is equal to one.
belongs to
Quantity c
has facts
description ap "generalized function on the real numbers"@en

Dirichlet Boundary Conditionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DirichletBoundaryCondition

belongs to
Mathematical Formulation c
has facts
description ap "boundary condition specifying the values that a solution of a differential equation needs to take along the boundaries of a domain"@en
alt Label ap "second-type boundary condition"@en
wikidata I D ap Q1193699 ep

Dirichlet Boundary Condition For Electric Potentialni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DirichletBoundaryConditionForElectricPotential

belongs to
Mathematical Formulation c
has facts
contains quantity op Electric Potential ni
contains quantity op Time ni
generalized by formulation op Dirichlet Boundary Condition ni
defining formulation dp "$\psi(r,t)|_{\Gamma_k}=\psi_{0}+U_k(t)$"^^La Te X ep
in defining formulation dp "$U_k$, Applied External Voltage"^^La Te X ep
in defining formulation dp "$\Gamma_k$, Electrode Interfaces"^^La Te X ep
in defining formulation dp "$\psi$, Electric Potential"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
description ap "Dirichlet boundary condition for the electric potential at an interface"@en

Dirichlet Boundary Condition For Electron Fermi Potentialni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DirichletBoundaryConditionForElectronFermiPotential

belongs to
Mathematical Formulation c
has facts
contains quantity op Applied External Voltage ni
contains quantity op Electrode Interfaces ni
contains quantity op Fermi Potential For Electrons ni
generalized by formulation op Dirichlet Boundary Condition ni
defining formulation dp "$\phi_n |_{\Gamma_k} = U_k$"^^La Te X ep
in defining formulation dp "$U_k$, Applied External Voltage"^^La Te X ep
in defining formulation dp "$\Gamma_k$, Electrode Interfaces"^^La Te X ep
in defining formulation dp "$\phi_n$, Fermi Potential For Electrons"^^La Te X ep
description ap "Fermi potential is given by applied external voltages at the Ohmic contacts, e.g. semiconductor-metal interfaces"@en

Dirichlet Boundary Condition For Hole Fermi Potentialni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DirichletBoundaryConditionForHoleFermiPotential

belongs to
Mathematical Formulation c
has facts
contains quantity op Applied External Voltage ni
contains quantity op Electrode Interfaces ni
contains quantity op Fermi Potential For Holes ni
generalized by formulation op Dirichlet Boundary Condition ni
defining formulation dp "$\phi_n |_{\Gamma_k} = U_k$"^^La Te X ep
in defining formulation dp "$U_k$, Applied External Voltage"^^La Te X ep
in defining formulation dp "$\Gamma_k$, Electrode Interfaces"^^La Te X ep
in defining formulation dp "$\phi_p$, Fermi Potential For Holes"^^La Te X ep
description ap "Fermi potential is given by applied external voltages at the Ohmic contacts, e.g. semiconductor-metal interfaces"@en

Discrete Element Methodni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Discrete_Element_Method

Describes any family of numerical functions for computing the motion and the effects of a large number of small particles. DEM is an effective method of addressing engineering problems in granular and discontinuous materials, especially in granular flows, powder mechanics, ice and rock mechanics.
belongs to
Mathematical Model c
has facts
invented in op Cundall (1979) A discrete numerical model for granular assemblies ni
description ap "family of numerical methods for computing the motion and effect of a large number of small particles"@en
wikidata I D ap Q902783 ep

Discrete Susceptible Infectious Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DiscreteSusceptibleInfectiousModel

belongs to
Mathematical Model c
has facts
models op Spreading of Infectious Diseases ni
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean
description ap "discrete model for the spreading of infectious diseases considering susceptible and infectious individuals"@en

Discrete Susceptible Infectious Removed Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DiscreteSusceptibleInfectiousRemovedModel

belongs to
Mathematical Model c
has facts
generalizes op Discrete Susceptible Infectious Model ni
models op Spreading of Infectious Diseases ni
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean
description ap "discrete model for the spreading of infectious diseases considering susceptible, infectious and recovered/removed individuals"@en
wikidata I D ap "https://www.wikidata.org/wiki/Q2206263"

Discrete Susceptible Infectious Susceptible Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DiscreteSusceptibleInfectiousSusceptibleModel

discrete-time model for the spreding of infectious diseases with temporary resistance considering susceptible and infectious individuals
belongs to
Mathematical Model c
has facts
discretizes op Continuous Susceptible Infectious Susceptible Model ni
models op Spreading of Infectious Diseases ni
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean
wikidata I D ap "https://www.wikidata.org/wiki/Q2351772"

Displacementni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Displacement

Vector that is the shortest distance from the initial to the final position of a point. In elasticity, displacements typically denote the motion of particles/matter from their equilibrium geometry
belongs to
Quantity c
has facts
generalized by quantity op Length ni
generalizes quantity op Displacement Muscle Tendon ni
generalizes quantity op Displacement Of Atoms ni
description ap "vector that is the shortest distance from the initial (equilibrium) to the final (current) position of a point"@en
qudt I D ap Displacement ep
wikidata I D ap Q190291 ep

Displacement Muscle Tendonni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DisplacementMuscleTendon

belongs to
Quantity c
has facts
generalized by quantity op Change In Length ni
generalized by quantity op Displacement ni
description ap "displacements of the muscle-tendon connection compared to the stress-free position"@en
wikidata I D ap Q190291 ep

Displacement Of Atomsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DisplacementOfAtoms

belongs to
Quantity c
has facts
contained in formulation op Darwin-Howie-Whelan Equation for a strained crystal ni
generalized by quantity op Length ni
description ap "displacement of atoms from their equilibrium positions in a non-rigid molecule or solid"@en

Dissociation Constantni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DissociationConstant

belongs to
Quantity c
has facts
description ap "measures the propensity of a larger object to separate (dissociate) reversibly into smaller components"@en
wikidata I D ap Q898254 ep

Dixon Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DixonEquationUniUniReactionwithoutProductandCompetitiveCompleteInhibitionSteadyStateAssumption

Dixon Equation for Uni Uni Reaction without Product and competitive complete Inhibition following Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption) ni
defining formulation dp "$\frac{1}{v_0} = \frac{1}{V_{max,f}}*(1+\frac{K_S}{c_S}) + \frac{K_S * c_I}{V_{max,f}*K_{ic}*c_S}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{ic}$, Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$, Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Dixon Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DixonEquationUniUniReactionwithoutProductandMixedCompleteInhibitionSteadyStateAssumption

Dixon Equation for Uni Uni Reaction without Product and mixed complete Inhibition following Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni
defining formulation dp "$$\frac{1}{v_0} = \frac{1}{V_{max,f}} * (1 + \frac{K_m}{c_S}) + \frac{c_I}{V_{max,f}} * (\frac{1}{K_{iu}} + \frac{K_m}{K_{ic}*c_S})$$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{ic}$, Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$K_{iu}$, Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$, Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Dixon Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DixonEquationUniUniReactionwithoutProductandNonCompetitiveCompleteInhibitionSteadyStateAssumption

Dixon Equation for Uni Uni Reaction without Product and non-competitive complete Inhibition following Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption) ni
similar to formulation op Dixon Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni
defining formulation dp "$$\frac{1}{v_0} = \frac{1}{V_{max,f}} * (1 + \frac{K_m}{c_S}) + \frac{c_I}{V_{max,f}} * (\frac{1}{K_{iu}} + \frac{K_m}{K_{ic}*c_S})$$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{ic}$, Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$K_{iu}$, Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$, Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Dixon Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DixonEquationUniUniReactionwithoutProductandUncompetitiveCompleteInhibitionSteadyStateAssumption

Dixon Equation for Uni Uni Reaction without Product and uncompetitive complete Inhibition following Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption) ni
defining formulation dp "$\frac{1}{v_0} = \frac{1}{V_{max,f}} * (1 + \frac{K_S}{c_S}) + \frac{c_I}{V_{max,f} * K_{iu}}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{iu}$, Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$, Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Doping Profileni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DopingProfile

belongs to
Quantity c
has facts
contained in formulation op Poisson Equation For The Electric Potential ni
description ap "intentional introduction of impurities into an intrinsic (undoped) semiconductor for the purpose of modulating its electrical, optical and structural properties"@en

Drag Coefficientni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DragCoefficient

belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
description ap "dimensionless parameter to quantify fluid resistance"@en
wikidata I D ap Q1778961 ep

Drift (Velocity)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Drift

Average velocity attained by particles due to external forces, e.g. when subjected to an electric field.
belongs to
Quantity c
has facts
generalized by quantity op Velocity ni
description ap "average velocity attained by particles due to external forces"@en
wikidata I D ap Q909891 ep

Durationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Duration

belongs to
Quantity c
has facts
generalized by quantity op Time ni
description ap "physical quantity for describing the temporal distance between events"@en
qudt I D ap Time ep
wikidata I D ap Q2199864 ep

Duration per Unitni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DurationPerUnit

Duration of an event per specific unit , e.g. duration per 1km, duration per length, duration of line,...
belongs to
Quantity c
has facts
generalized by quantity op Duration ni
description ap "duration of an event per specific unit"@en

Dynamical Electron Scattering Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#DynamicalElectronScatteringModel

In crystalline solids, e.g. semiconductor nanostructures, it is influenced by spatial variations in the material composition and by local deformations of the lattice due to elastic strain. In order to model TEM images, we need to use elasticity theory to obtain the strain profile and couple this with the equations describing the electron propagation through the sample.
belongs to
Mathematical Model c
has facts
contains boundary condition op Neumann Boundary Condition (Stress-Free Relaxation) ni
contains formulation op Hooke Law (Linear Elasticity) ni
contains formulation op Momentum Balance Equation ni
generalized by model op Quantum Model (Closed System) ni
description ap "quantum-mechanical propagation of electrons through a sample governed by dynamical electron scattering"@en
doi I D ap s11082 020 02356 y ep

Eadie (1942) The Inhibition of Cholinesterase by Physostigmine and Prostigmineni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Eadie_1942_The_Inhibition_of_Cholinesterase_by_Physostigmine_and_Prostigmine

belongs to
Publication c
has facts
invents op Uni Uni Reaction (Eadie Hofstee Model without Product - Irreversibility Assumption) ni
invents op Uni Uni Reaction (Eadie Hofstee Model without Product - Rapid Equilibrium Assumption) ni
invents op Uni Uni Reaction (Eadie Hofstee Model without Product - Steady State Assumption) ni
doi I D ap S0021 9258(18)72452 6 ep

Eadie Hofstee Equation (Uni Uni Reaction without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EadieHofsteeEquationforUniUniReactionwithoutProductSteadyStateAssumption

Eadie Hofstee Equation for Uni Uni Reaction without Product following Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product - Steady State Assumption) ni
defining formulation dp "$v_0 = V_{max,f} - K_S * \frac{v_0}{c_S}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Eadie Hofstee Equation (Uni Uni Reaction without Product - Irreversibility Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EadieHofsteeEquationforUniUniReactionwithoutProductIrreversibilityAssumption

Eadie Hofstee Equation for Uni Uni Reaction without Product following Irreversibility Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Irreversibility Assumption) ni
contains quantity op Substrate Concentration ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product - Irreversibility Assumption) ni
defining formulation dp "$v_0 = V_{max,f} - K_S * \frac{v_0}{c_S}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Irreversibility Assumption)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Eadie Hofstee Equation (Uni Uni Reaction without Product - Rapid Equilibrium Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EadieHofsteeEquationforUniUniReactionwithoutProductRapidEquilibriumAssumption

Eadie Hofstee Equation for Uni Uni Reaction without Product following Rapid Equilibrium Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Rapid Equilibrium Assumption) ni
contains quantity op Substrate Concentration ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product - Rapid Equilibrium Assumption) ni
defining formulation dp "$v_0 = V_{max,f} - K_S * \frac{v_0}{c_S}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Rapid Equilibrium Assumption)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Eadie Hofstee Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EadieHofsteeEquationUniUniReactionwithoutProductandCompetitiveCompleteInhibitionSteadyStateAssumption

Eadie Hofstee Equation for Uni Uni Reaction without Product and competitive complete Inhibition following Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption) ni
defining formulation dp "$v_0 = V_{max,f} - K_S * (1 + \frac{c_I}{K_{ic}}) * \frac{v_0}{c_S}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{ic}$, Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$, Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Eadie Hofstee Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EadieHofsteeEquationUniUniReactionwithoutProductandMixedCompleteInhibitionSteadyStateAssumption

Eadie Hofstee Equation for Uni Uni Reaction without Product and mixed complete Inhibition following Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni
defining formulation dp "$$v_0 = \frac{V_{max,f}}{1+\frac{c_I}{K_{iu}}} - \frac{K_m * (1+\frac{c_I}{K_{ic}})}{1+\frac{c_I}{K_{iu}}} * \frac{v_0}{c_S}$$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{ic}$, Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$K_{iu}$, Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$, Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Eadie Hofstee Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EadieHofsteeEquationUniUniReactionwithoutProductandNonCompetitiveCompleteInhibitionSteadyStateAssumption

Eadie Hofstee Equation for Uni Uni Reaction without Product and non-competitive complete Inhibition following Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption) ni
similar to formulation op Eadie Hofstee Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni
defining formulation dp "$$v_0 = \frac{V_{max,f}}{1+\frac{c_I}{K_{iu}}} - \frac{K_m * (1+\frac{c_I}{K_{ic}})}{1+\frac{c_I}{K_{iu}}} * \frac{v_0}{c_S}$$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{ic}$, Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$K_{iu}$, Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$, Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Eadie Hofstee Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EadieHofsteeEquationUniUniReactionwithoutProductandUncompetitiveCompleteInhibitionSteadyStateAssumption

Eadie Hofstee Equation for Uni Uni Reaction without Product and uncompetitive complete Inhibition following Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption) ni
defining formulation dp "$v_0 = \frac{V_{max,f}}{1 + \frac{c_I}{K_{iu}}} - \frac{K_S}{1 + \frac{c_I}{K_{iu}}} * \frac{v_0}{c_S}$"^^La Te X ep
in defining formulation dp "$K_S$,Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{iu}$,Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$,Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$,Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$,Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$,Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Earth Massni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EarthMass

Mass of the planet Earth: 5.9722×1024 kg, with a relative uncertainty of 10−4
belongs to
Quantity c
has facts
generalized by quantity op Mass ni
description ap "mass of the planet Earth"@en
wikidata I D ap Q25935139 ep

Earth Radiusni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EarthRadius

mean distance from the Earth's center to its surface: A globally-average value is usually considered to be 6,371 kilometres with a 0.3% variability (±10 km)
belongs to
Quantity c
has facts
generalized by quantity op Length ni
description ap "mean distance from the Earth's center to its surface"@en
wikidata I D ap Q1155470 ep

Effective Conductivityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EffectiveConductivity

Effective conductivity refers to the combined effects of conduction, convection, and radiation heat transfer within an enclosed space or material and measures how effectively the medium can transfer heat.
belongs to
Quantity c
has facts
generalized by quantity op Electric Conductivity ni
description ap "combined effects of conduction, convection, and radiation heat transfer within an enclosed space or material"@en

Effective Massni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EffectiveMass

The mass that a particle appears to have when responding to forces, or the mass that it seems to have when interacting with other identical particles.
belongs to
Quantity c
has facts
generalized by quantity op Mass ni
description ap "mass that a particle appears to have when responding to forces"@en
qudt I D ap Effective Mass ep
wikidata I D ap Q1064434 ep

Effective Mass (Solid-State Physics)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EffectiveMassSolidStatePhysics

In solid state physics, effective electron masses are deduced from band structure calculations (curvature of bands). In certain cases, these masses can have negative values. Their absolute values are typically found between 0.01 and 10 times the mass of a free electron.
belongs to
Quantity c
has facts
generalized by quantity op Effective Mass ni
description ap "effective electron masses are deduced from band structure calculations (curvature of bands)"@en
wikidata I D ap Q1064434 ep

Effective Mass (Spring-Mass System)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EffectiveMassSpringMassSystem

belongs to
Quantity c
has facts
generalized by quantity op Effective Mass ni
description ap "mass that needs to be added to a particle mass to correctly predict the behavior of the system"@en
wikidata I D ap Q3509437 ep

Efficient Numerical Simulation of Soil-Tool Interactionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Efficient_Numerical_Simulation_of_Soil-Tool_Interaction

belongs to
Research Problem c
has facts
contained in field op Civil Engineering ni
modeled by op Recurrent Neural Network Surrogate for Discrete Element Method ni
studied in op Jahnke (2022) Efficient Numerical Simulation of Soil-Tool Interaction ni

Egyptologyni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Egyptology

belongs to
Research Field c
has facts
description ap "scientific study of ancient Egypt"@en
mardi I D ap Item: Q6032633 ep
wikidata I D ap Q145903 ep

Eigenstress Of Crystalni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EigenStressOfCrystal

belongs to
Quantity c
has facts
generalized by quantity op Stress Of Crystal ni
description ap "eigenstress of a crystal (stress-free condition) used in theory of elasticity"@en

Elastic Stiffness Tensorni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElasticStiffnessTensor

Elastic Stiffness Tensor, used e.g. in Hook's Law for the elastic deformation of a solid.
belongs to
Quantity c
has facts
description ap "fourth-order tensor that describes the relationship between stress and strain in a material"@en

Electric Capacitanceni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Capacitance

Ability of a body to store electrical charge
belongs to
Quantity Kind c
has facts
qudt I D ap Capacitance ep
wikidata I D ap Q164399 ep

Electric Chargeni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElectricCharge

Physical property that quantifies an object's interaction with electric fields
belongs to
Quantity Kind c
has facts
qudt I D ap Electric Charge ep
wikidata I D ap Q1111 ep

Electric Charge Densityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElectricChargeDensity

belongs to
Quantity c
has facts
generalizes quantity op Density Of Holes ni
similar to quantity op Density Of Electrons ni
similar to quantity op Density Of Holes ni
description ap "electric charge per volume"@en
wikidata I D ap Q69425629 ep

Electric Conductivityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElectricConductivity

physical quantity and property of material describing how readily a given material allows the flow of electric current
belongs to
Quantity Kind c
has facts
qudt I D ap Conductivity.html ep
wikidata I D ap Q4593291 ep

Electric Constantni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElectricConstant

belongs to
Quantity c
is same as
Permittivity (Vacuum) ni
has facts
same As ep Permittivity (Vacuum) ni
description ap "physical constant that represents the capability of the vacuum to permit electric field lines"@en
qudt I D ap Electric Constant ep

Electric Currentni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElectricCurrent

Base quantity of the International System of Quantities (ISQ), measured in ampere (A)
belongs to
Quantity Kind c
has facts
qudt I D ap Electric Current ep
wikidata I D ap Q29996 ep

Electric Current Densityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElectricCurrentDensity

belongs to
Quantity c
has facts
similar to quantity op Flux Of Electrons ni
similar to quantity op Flux Of Holes ni
description ap "electric current per area of cross section"@en
wikidata I D ap Q234072 ep

Electric Dipole Momentni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElectricDipoleMoment

vector physical quantity measuring the separation of positive and negative electrical charges within a system
belongs to
Quantity Kind c
has facts
wikidata I D ap Q735135 ep

Electric Fieldni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElectricField

Vector field representing the force applied to a charged test particle. The electric field is the gradient of the electrostatic potential
belongs to
Quantity Kind c
has facts
qudt I D ap Electric Field Strength ep
wikidata I D ap Q46221 ep

Electric Polarizabilityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElectricPolarizability

Tendency of matter subjected to an electric field to acquire an electric dipole moment. When subject to an electric field, the negatively charged electrons and positively charged atomic nuclei are subject to opposite forces and undergo charge separation.
belongs to
Quantity Kind c
has facts
similar to quantity op Permittivity (Dielectric) ni
wikidata I D ap Q869891 ep

Electric Potentialni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElectricPotential

belongs to
Quantity c
has facts
contained in formulation op Poisson Equation For The Electric Potential ni
generalized by quantity op Voltage ni
description ap "electric field is the gradient of the electrostatic potential"@en
alt Label ap "Electrostatic Potential"@en
qudt I D ap Electric Potential ep
wikidata I D ap Q55451 ep

Electric Potential Fourier Coefficientsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElectricPotentialFourierCoefficients

belongs to
Quantity c
has facts
contained in formulation op Darwin-Howie-Whelan Equation for an unstrained crystal ni
contained in formulation op Darwin-Howie-Whelan Equation for a strained crystal ni
similar to quantity op Electric Potential ni
description ap "coefficients in a Fourier expansion of the electric potential"

Electrode Interfacesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElectrodeInterfaces

Positions of the electrode interfaces. Typically used to specify boundary conditions for electric fields or electron|hole densities in semiconductor-metal interfaces (Ohmic contacts)
belongs to
Quantity c
has facts
contained in formulation op Dirichlet Boundary Condition For Electric Potential ni
generalized by quantity op Length ni
description ap "positions of the electrode interfaces"@en
wikidata I D ap Q3783831 ep

Electrodynamicsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Electrodynamics

belongs to
Research Field c
is same as
Electromagnetism ni
has facts
same As ep Electromagnetism ni

Electromagnetic Fields And Wavesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElectromagneticFieldsAndWaves

Shalva: Given the initial fields E(r, t = 0) and B(r, t = 0), given full charge density ρ(r, t) and the current density j(r, t), find the electric and magnetic fields, E(r, t) and B(r, t).
belongs to
Research Problem c
has facts
modeled by op Maxwell Equations Model ni
description ap "physical fields produced by electrically charged objects"@en
wikidata I D ap Q177625 ep

Electromagnetismni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Electromagnetism

branch of theoretical physics that studies consequences of the electromagnetic fields, waves, and forces between electric charges and currents
belongs to
Research Field c
is same as
Electrodynamics ni
has facts
contains problem op Electromagnetic Fields And Waves ni
wikidata I D ap Q377930 ep

Electron Massni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElectronMass

In particle physics, the mass of a stationary electron, also known as the invariant mass of the electron. It is one of the fundamental constants of physics.
belongs to
Quantity c
has facts
generalized by quantity op Mass ni
description ap "mass of a stationary electron"@en
qudt I D ap Electron Mass ep
wikidata I D ap Q3814108 ep

Electron Shuttling Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElectronShuttlingModel

Quantum dynamical modeling of an electron to be shuttled, governed by the electric potential generated by the clavier (and other) gates in a Silicon QuBus device. Spin and valley states as well as the respective interactions are neglected. Moreover, the current model is limited to the coherent wave packet evolution and disregards the effects of noise and dissipation.
belongs to
Mathematical Model c
has facts
contains boundary condition op Dirichlet Boundary Condition For Electric Potential ni
contains boundary condition op Neumann Boundary Condition For Electric Potential ni
contains boundary condition op Periodic Boundary Condition For Electric Potential ni
contains formulation op Laplace Equation For The Electric Potential ni
contains formulation op Quantum Hamiltonian (Electric Charge) ni
contains formulation op Quantum Lindblad Equation ni
contains formulation op Quantum Liouville Equation ni
contains formulation op Schrödinger Equation (Time Dependent) ni
contains formulation op Schrödinger Equation (Time Independent) ni
generalized by model op Control System Model (Bilinear) ni
generalized by model op Quantum Model (Closed System) ni
models op Spin Qbit Shuttling ni
description ap "quantum dynamical model of an electron to be shuttled in a Silicon QuBus device"@en
doi I D ap W I A S. P R E P R I N T.3082 ep

Electrophysiological Muscle Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Electrophysiological_Muscle_Model

belongs to
Mathematical Model c
has facts
studied in op Homs-Pons (2024) Coupled simulations and parameter inversion for neural system and electrophysiological muscle models ni
description ap "mathematical model of the neuromuscular system combining continuum mechanics models with electrophysiological models"@en
doi I D ap gamm.202370009 ep

Electrophysiological Muscle ODE Systemni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Electrophysiological_Muscle_Model_ODE_System

One continuum mechanics three-dimensional model for each participant. The equations originate from conservation of mass and momentum for each participant.
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Electrophysiological Muscle Model ni
contains formulation op Lumped Activation Parameter ni
contains quantity op Displacement Muscle Tendon ni
contains quantity op Material Density ni
contains quantity op Material Point Acceleration ni
contains quantity op Material Point Velocity ni
contains quantity op Pressure ni
contains quantity op Stress Tensor (Piola-Kirchhoff) ni
contains quantity op Time ni
defining formulation dp "$$\begin{align*} \rho_{\text{M}1} \mathbf{\ddot{x}}_{\text{M}1} &= \mathbf{\nabla} \cdot \left(\mathbf{P}_{\text{passive}}(\mathbf{F}_{\text{M}1}) + \mathbf{P}_{\text{active}}(\mathbf{F}_{\text{M}1}, \gamma_{\text{M}1}) - p_{\text{M}1}\mathbf{F}^{-T}_{\text{M}1} \right), &\text{div $\mathbf{\dot{x}}_{\text{M}1} = 0$} ~ &\text{in $\Omega_{\text{M}1}\times [0,T_{\text{end}})$}\\ \rho_{\text{M}2} \mathbf{\ddot{x}}_{\text{M}2} &= \mathbf{\nabla} \cdot \left(\mathbf{P}_{\text{passive}}(\mathbf{F}_{\text{M}2}) + \mathbf{P}_{\text{active}}(\mathbf{F}_{\text{M}2}, \gamma_{\text{M}2}) - p_{\text{M}2}\mathbf{F}^{-T}_{\text{M}2} \right), &\text{div $\mathbf{\dot{x}}_{\text{M}2} = 0$} ~ &\text{in $\Omega_{\text{M}2}\times [0,T_{\text{end}})$}\\ \rho_{\text{T}}\mathbf{\ddot{x}}_\text{T}&= \mathbf{\nabla} \cdot \left(\mathbf{P}_\text{passive}(\mathbf{F}_{\text{T}}) - p_\text{T}\mathbf{F}^{-T}_{\text{T}}\right), &\text{div $\mathbf{\dot{x}}_{\text{T}}=0$}& ~\text{in $\Omega_{\text{T}}\times [0,T_{\text{end}})$} \end{align*}$$"^^La Te X ep
in defining formulation dp "$\ddot{\mathbf{x}}$, Material Point Acceleration"^^La Te X ep
in defining formulation dp "$\dot{\mathbf{x}}$, Material Point Velocity"^^La Te X ep
in defining formulation dp "$\gamma$, Lumped Activation Parameter"^^La Te X ep
in defining formulation dp "$\mathbf{P}$, Stress Tensor (Piola-Kirchhoff)"^^La Te X ep
in defining formulation dp "$\mathbf{x}$, Displacement Muscle Tendon"^^La Te X ep
in defining formulation dp "$\rho$, Material Density"^^La Te X ep
in defining formulation dp "$p$, Pressure"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
description ap "three-dimensional electrophysiological model for a muscle"@en

Elementary Chargeni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElementaryCharge

belongs to
Quantity c
has facts
contained in formulation op Poisson Equation For The Electric Potential ni
generalized by op Electric Charge ni
description ap "electric charge carried by a single proton or a single positron"@en
qudt I D ap Elementary Charge ep
wikidata I D ap Q2101 ep

Empirical Distribution Of Individualsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EmpiricalDistributionOfIndividuals

Empirical distribution of individuals that follow a specific medium and influencer at a given time by the sum of Dirac Delta distributions $\delta$ placed at the individuals’ opinions. Subscript m denotes the medium and subscript l denotes the Influencer
belongs to
Quantity c
has facts
description ap "empirical distribution of individuals that follow a specific medium and influencer"@en

Empirical Distribution Of Individuals Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EmpiricalDistributionOfIndividualsFormulation

Empirical distribution of individuals that follow a medium m and influencer l at time t by the sum of Dirac Delta distributions $\delta$ placed at the individuals’ opinions. This distribution describes the stochastic opinion instances at a given time and integrates to $\int_D \rho_{m, l}^{(N)}(x, t) d x=: n_{m, l}^{(N)}(t)$, the proportion of individuals that follow medium m and influencer l.
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Partial Mean Field Opinion Model ni
contains quantity op Dirac Delta Distribution ni
contains quantity op Empirical Distribution Of Individuals ni
contains quantity op Influencer Individual Matrix ni
contains quantity op Medium Follower Matrix ni
contains quantity op Opinion ni
contains quantity op Time ni
contains quantity op Total Number Of Individuals ni
defining formulation dp "$\rho_{m, l}^{(N)}(x, t)=\frac{1}{N} \sum_{\substack{i: B_{i m}=1 \\ C_{i l}(t)=1}} \delta\left(x-x_i(t)\right)$"^^La Te X ep
in defining formulation dp "$B_im$, Medium Follower Matrix"^^La Te X ep
in defining formulation dp "$C_im$, Influencer Individual Matrix"^^La Te X ep
in defining formulation dp "$N$, Total Number Of Individuals"^^La Te X ep
in defining formulation dp "$\delta$, Dirac Delta Distribution"^^La Te X ep
in defining formulation dp "$\rho_{m, l}^{(N)}$, Empirical Distribution Of Individuals"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$x$, Opinion"^^La Te X ep
in defining formulation dp "$x_i$, Opinion"^^La Te X ep

Energyni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Energy

Quantitative property of a physical system, recognizable in the performance of work and in the form of heat and light
belongs to
Quantity Kind c
has facts
qudt I D ap Energy ep
wikidata I D ap Q11379 ep

Enzyme - Product 1 - Complex Concentration ODE (Bi Bi Reaction Ordered with single central Complex)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Enzyme-Product1ComplexConcentrationODEBiBiOrderedsingleCC

Ordinary differential equation describing the enzyme - product 1 - complex concentration over time in a bi bi enzymatic reaction following the ordered mechanism with a single central Complex.
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{EP_1}}{dt} = k_{4} * c_{ES_{1}S_{2}=EP_{1}P_{2}} + k_{-5} * c_{E} * c_{P_1} - k_{-4} * c_{EP_1} * c_{P_2} - k_{5} * c_{EP_1}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{EP_{1}}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{EP_{1}}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_{1}S_{2}=EP_{1}P_{2}}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_{1}}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_{2}}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-5}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{5}$, Reaction Rate Constant"^^La Te X ep

Enzyme - Product 1 - Complex Concentration ODE (Bi Bi Reaction Ordered)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Enzyme-Product1ComplexConcentrationODEBiBiOrdered

Ordinary differential equation describing the enzyme - product 1 - complex concentration over time in a bi bi enzymatic reaction following the ordered mechanism.
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{EP_1}}{dt} = k_{4} * c_{EP_{1}P_{2}} + k_{-5} * c_{E} * c_{P_1} - k_{-4} * c_{EP_1} * c_{P_2} - k_{5} * c_{EP_1}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{EP_{1}}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{EP_{1}P_{2}}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{EP_{1}}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_{1}}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_{2}}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-5}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{5}$, Reaction Rate Constant"^^La Te X ep

Enzyme - Product 1 - Product 2 - Complex Concentration ODE (Bi Bi Reaction Ordered)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Enzyme-Product1-Product2ComplexConcentrationODEBiBiOrdered

Ordinary differential equation describing the enzyme - product 1 - product 2 - complex concentration over time in a bi bi enzymatic reaction following the ordered mechanism.
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{EP_{1}P_{2}}}{dt} = k_{3} * c_{ES_{1}S_{2}} + k_{-4} * c_{EP_1} * c_{P_2} - k_{-3} * c_{EP_{1}P_{2}} - k_{4} * c_{EP_{1}P_{2}}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{EP_{1}P_{2}}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{EP_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{EP_{1}P_{2}}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_{1}S_{2}}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep

Enzyme - Product 1 - Product 2 Complex Concentrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EnzymeProduct1Product2ComplexConcentration

belongs to
Quantity c
has facts
generalized by quantity op Concentration ni
description ap "amount of enzyme - product 1 - product 2 complex present in a reaction environment"@en

Enzyme - Product 1 Complex Concentrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EnzymeProduct1ComplexConcentration

belongs to
Quantity c
has facts
generalized by quantity op Concentration ni
description ap "amount of enzyme - product 1 complex present in a reaction environment"@en

Enzyme - Product 2 - Complex Concentration ODE (Bi Bi Reaction Theorell-Chance)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Enzyme-Product2ComplexConcentrationODEBiBiTheorellChance

Ordinary differential equation describing the enzyme - product 2 - complex concentration over time in a bi bi enzymatic reaction following the Theorell-Chance mechanism.
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{EP_2}}{dt} = k_{2} * c_{ES_1} * c_{S_2} + k_{-3} * c_{E} * c_{P_2} - k_{-2} * c_{EP_2} * c_{P_1} - k_3 * c_{EP_2}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{EP_2}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{EP_2}}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep

Enzyme - Product 2 Complex Concentrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EnzymeProduct2ComplexConcentration

belongs to
Quantity c
has facts
generalized by quantity op Concentration ni
description ap "amount of enzyme - product 2 complex present in a reaction environment"@en

Enzyme - Substrate - Complex Concentration ODE (Uni Uni Reaction)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EnzymeSubstrateComplexConcentrationODEUniUni

ODE describing a change of concentration of Enzyme-Substrate complex in an Uni Uni reaction over time
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{ES}}{dt}=k_{1}*c_{E}*c_{S}-k_{-1}*c_{ES}-k_{2}*c_{ES}+k_{-2}*c_{E}*c_{P}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{ES}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{ES}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Enzyme - Substrate 1 - Complex Concentration ODE (Bi Bi Reaction Ordered with single central Complex)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Enzyme-Substrate1ComplexConcentrationODEBiBiOrderedsingleCC

Ordinary differential equation describing the enzyme - substrate 1 - complex concentration over time in a bi bi enzymatic reaction following the ordered mechanism with a single central Complex..
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{ES_1}}{dt} = k_{1} * c_{E} * c_{S_1} + k_{-2} * c_{ES_{1}S_{2}=EP_{1}P_{2}} - k_{-1} * c_{ES_1} - k_2 * c_{ES_1} * c_{S_2}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{ES_1}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_{1}S_{2}=EP_{1}P_{2}}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep

Enzyme - Substrate 1 - Complex Concentration ODE (Bi Bi Reaction Ordered)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Enzyme-Substrate1ComplexConcentrationODEBiBiOrdered

Ordinary differential equation describing the enzyme - substrate 1 - complex concentration over time in a bi bi enzymatic reaction following the ordered mechanism.
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{ES_1}}{dt} = k_{1} * c_{E} * c_{S_1} + k_{-2} * c_{ES_{1}S_{2}} - k_{-1} * c_{ES_1} - k_2 * c_{ES_1} * c_{S_2}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{ES_1}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_{1}S_{2}}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep

Enzyme - Substrate 1 - Complex Concentration ODE (Bi Bi Reaction Ping Pong)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Enzyme-Substrate1ComplexConcentrationODEBiBiPingPong

Ordinary differential equation describing the enzyme - substrate 1 - complex concentration over time in a bi bi enzymatic reaction following the ping pong mechanism.
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{ES_1}}{dt} = k_{1} * c_{E} * c_{S_1} + k_{-2} * c_{E*} * c_{P_1} - k_{-1} * c_{ES_1} - k_{2} c_{ES_1}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{ES_1}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{E*}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep

Enzyme - Substrate 1 - Complex Concentration ODE (Bi Bi Reaction Theorell-Chance)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Enzyme-Substrate1ComplexConcentrationODEBiBiTheorellChance

Ordinary differential equation describing the enzyme - substrate 1 - complex concentration over time in a bi bi enzymatic reaction following the Theorell-Chance mechanism.
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{ES_1}}{dt} = k_{1} * c_{E} * c_{S_1} + k_{-2} * c_{EP_{2}} * c_{P_1} - k_{-1} * c_{ES_1} - k_2 * c_{ES_1} * c_{S_2}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{ES_1}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{EP_2}}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep

Enzyme - Substrate 1 - Substrate 2 - Complex Concentration ODE (Bi Bi Reaction Ordered)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Enzyme-Substrate1-Substrate2ComplexConcentrationODEBiBiOrdered

Ordinary differential equation describing the enzyme - substrate 1 - substrate 2 - complex concentration over time in a bi bi enzymatic reaction following the ordered mechanism.
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{ES_{1}S_{2}}}{dt} = k_{2} * c_{ES_1} * c_{S_2} + k_{-3} * c_{EP_{1}P_{2}} - k_{-2} * c_{ES_{1}S_{2}} - k_{3} * c_{ES_{1}S_{2}}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{ES_{1}S_{2}}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{EP_{1}P_{2}}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_{1}S_{2}}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep

Enzyme - Substrate 1 - Substrate 2 = Enzyme - Product 1 - Product 2 - Complex Concentration ODE (Bi Bi Reaction Ordered with single central Complex)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Enzyme-Substrate1-Substrate2Enzyme-Product1-Product2-ComplexConcentrationODEBiBiOrderedsingleCC

Ordinary differential equation describing the enzyme - substrate 1 - substrate 2 = enzyme - product 1 - product 2 - complex concentration over time in a bi bi enzymatic reaction following the ordered mechanism with a single central Complex.
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{ES_{1}E_{2}=EP_{1}P_{2}}}{dt} = k_2 * c_{ES_1} * c_{S_2} - k_{-2} * c_{ES_{1}E_{2}=EP_{1}P_{2}} - k_4 * c_{ES_{1}E_{2}=EP_{1}P_{2}} + k_{-4} * c_{EP_1} * c_{P_2}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{ES_{1}S_{2}=EP_{1}P_{2}}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{EP_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_{1}S_{2}=EP_{1}P_{2}}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep

Enzyme - Substrate 1 - Substrate 2 = Enzyme - Product 1 - Product 2 Complex Concentrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EnzymeSubstrate1Substrate2EnzymeProduct1Product2ComplexConcentration

belongs to
Quantity c
has facts
generalized by quantity op Concentration ni
description ap "amount of enzyme - substrate 1 - substrate 2 = enzyme -product 1 - product 2 complex present in a reaction environment"@en

Enzyme - Substrate 1 - Substrate 2 Complex Concentrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EnzymeSubstrate1Substrate2ComplexConcentration

belongs to
Quantity c
has facts
generalized by quantity op Concentration ni
description ap "amount of enzyme - substrate 1 - substrate 2 complex present in a reaction environment"@en

Enzyme - Substrate 1 Complex Concentrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EnzymeSubstrate1ComplexConcentration

belongs to
Quantity c
has facts
generalized by quantity op Concentration ni
description ap "amount of enzyme - substrate 1 complex present in a reaction environment"@en

Enzyme Concentrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EnzymeConcentration

belongs to
Quantity c
has facts
generalized by quantity op Concentration ni
description ap "amount of enzyme present in a reaction environment"@en

Enzyme Concentration ODE (Bi Bi Reaction Ordered with single central Complex)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EnzymeConcentrationODEBiBiOrderedsingleCC

Ordinary differential equation describing the enzyme concentration over time in a bi bi enzymatic reaction following the ordered mechanism with a single central Complex.
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{E}}{dt} = k_{-1} * c_{ES_1} + k_5 * c_{EP_1} - k_{1} * c_{E} * c_{S_1} - k_{-5} * c_{E} * c_{P_1}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{E}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{EP_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-5}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{5}$, Reaction Rate Constant"^^La Te X ep

Enzyme Concentration ODE (Bi Bi Reaction Ordered)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EnzymeConcentrationODEBiBiOrdered

Ordinary differential equation describing the enzyme concentration over time in a bi bi enzymatic reaction following the ordered mechanism.
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{E}}{dt} = k_{-1} * c_{ES_1} + k_5 * c_{EP_1} - k_{1} * c_{E} * c_{S_1} - k_{-5} * c_{E} * c_{P_1}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{E}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{EP_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-5}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{5}$, Reaction Rate Constant"^^La Te X ep

Enzyme Concentration ODE (Bi Bi Reaction Ping Pong)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EnzymeConcentrationODEBiBiPingPong

Ordinary differential equation describing the enzyme concentration over time in a bi bi enzymatic reaction following the ping pong mechanism.
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{E}}{dt} = k_{-1} * c_{ES_1} + k_{4} * c_{E*S_2} - k_{1} * c_{E} * c_{S_1} - k_{-4} * c_{E} * c_{P_2}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{E}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{E*S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep

Enzyme Concentration ODE (Bi Bi Reaction Theorell-Chance)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EnzymeConcentrationODEBiBiTheorellChance

Ordinary differential equation describing the enzyme concentration over time in a bi bi enzymatic reaction following the Theorell-Chance mechanism.
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{E}}{dt} = k_{-1} * c_{ES_1} + k_3 * c_{EP_2} - k_{1} * c_{E} * c_{S_1} - k_{-3} * c_{E} * c_{P_2}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{E}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{EP_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep

Enzyme Concentration ODE (Uni Uni Reaction)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EnzymeConcentrationODEUniUni

ODE desctibing a change in concentration of an Enzyme in an Uni Uni reaction over time
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{E}}{dt}=-k_{1}*c_{E}*c_{S}+k_{-1}*c_{ES}+k_{2}*c_{ES}-k_{-2}*c_{E}*c_{P}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{E}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{ES}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep

Enzyme Conservationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EnzmeConservation

Enzyme molecules are neither formed nor destroyed during the reaction, i.e. the initial enzyme concentration $c_{E_{0}}$ is, at any time, equal to the sum of free $c_{E}$ and bound enzyme $c_{EX}$ concentrations.
belongs to
Mathematical Formulation c
has facts
contains initial condition op Initial Enzyme Concentration (Uni Uni Reaction - Michaelis Menten Model) ni
contains quantity op Complexed Enzyme Concentration ni
contains quantity op Enzyme Concentration ni
defining formulation dp "$c_{E_{0}} = c_{E} + c_{EX}$"^^La Te X ep
in defining formulation dp "$c_{EX}$, Complexed Enzyme Concentration"^^La Te X ep
in defining formulation dp "$c_{E_{0}}$, Enzyme Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Enzyme Concentration"^^La Te X ep

Enzyme Kineticsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EnzymeKinetics

belongs to
Research Field c
has facts
contains problem op Bi Bi Reaction ni
description ap "study of rates of enzyme-catalyzed reactions"@en
wikidata I D ap Q883112 ep

Enzyme-Substrate Complex Concentrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EnzymeSubstrateComplexConcentration

belongs to
Quantity c
has facts
generalized by quantity op Complexed Enzyme Concentration ni
generalized by quantity op Concentration ni
description ap "amount of enzyme-substrate complex present in a reaction environment"@en

Epidemiologyni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Epidemiology

belongs to
Research Field c
has facts
description ap "study of the patterns, causes, and effects of health and disease conditions"@en
wikidata I D ap Q133805 ep

Equilibrium Constantni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EquilibriumConstant

belongs to
Quantity c
has facts
description ap "equilibrium constant of a chemical reaction is the value of its reaction quotient at chemical equilibrium, a state approached after sufficient time"@en
wikidata I D ap Q857809 ep

Equilibrium Constant (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EquilibriumConstantBiBiReactionOrderedSingleCCSS

belongs to
Mathematical Formulation c
has facts
contains quantity op Equilibrium Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{eq} = \frac{k_1 * k_2 * k_4 * k_5}{k_{-1} * k_{-2} * k_{-4} * k_{-5}}$"^^La Te X ep
in defining formulation dp "$K_{eq}$, Equilibrium Constant"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-5}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{5}$, Reaction Rate Constant"^^La Te X ep

Equilibrium Constant (Bi Bi Reaction Ordered - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EquilibriumConstantBiBiReactionOrderedSS

belongs to
Quantity c
has facts
defined by op Equilibrium Constant (Bi Bi Reaction Ordered - Steady State Assumption) (Definition) ni
generalized by quantity op Equilibrium Constant ni
is dimensionless dp "true"^^boolean
description ap "equilibrium constant of bi bi rection following ordered mechnism with steady state assumption"@en

Equilibrium Constant (Bi Bi Reaction Ordered - Steady State Assumption) (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EquilibriumConstantBiBiReactionOrderedSSDefinition

Definition of Equlibrium Constant of Bi Bi Reaction following Ordered Mechanism and Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Equilibrium Constant (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{eq} \equiv \frac{k_1 * k_2 * k_3 * k_4 * k_5}{k_{-1} * k_{-2} * k_{-3} * k_{-4} * k_{-5}}$"^^La Te X ep
in defining formulation dp "$K_{eq}$, Equilibrium Constant (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-5}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{5}$, Reaction Rate Constant"^^La Te X ep

Equilibrium Constant (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EquilibriumConstantBiBiReactionPingPongSS

belongs to
Mathematical Formulation c
has facts
contains quantity op Equilibrium Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{eq} = \frac{k_{1} * k_{2} * k_{3} * k_{4}}{k_{-1} * k_{-2} * k_{-3} *k_{-4}}$"^^La Te X ep
in defining formulation dp "$K_{eq}$, Equilibrium Constant"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep

Equilibrium Constant (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EquilibriumConstantBiBiReactionTheorellChanceSS

belongs to
Mathematical Formulation c
has facts
contains quantity op Equilibrium Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{eq} = \frac{k_1 * k_2 * k_3}{k_{-1} * k_{-2} * k_{-3}}$"^^La Te X ep
in defining formulation dp "$K_{eq}$, Equilibrium Constant"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep

Equivalance Equation Placeholderni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EquivalanceEquationPlaceholder

belongs to
Mathematical Formulation c
has facts
contained as formulation in op PDE SEIR Model ni
contains quantity op Diffusion Coefficient ni
contains quantity op Fraction Of Population Density Of Exposed ni
contains quantity op Fraction Of Population Density Of Infectious ni
contains quantity op Fraction Of Population Density Of Removed ni
contains quantity op Fraction Of Population Density Of Susceptibles ni
contains quantity op Unit Normal Vector ni
defining formulation dp "$\nu^T D \nabla s & =\nu^T D \nabla e=\nu^T D \nabla i=\nu^T D \nabla r=0$"^^La Te X ep
in defining formulation dp "$D$, Diffusion Coefficient"^^La Te X ep
in defining formulation dp "$\nu$, Unit Normal Vector"^^La Te X ep
in defining formulation dp "$e$, Fraction Of Population Density Of Exposed"^^La Te X ep
in defining formulation dp "$i$, Fraction Of Population Density Of Infectious"^^La Te X ep
in defining formulation dp "$r$, Fraction Of Population Density Of Removed"^^La Te X ep
in defining formulation dp "$s$, Fraction Of Population Density Of Susceptibles"^^La Te X ep

Ermoneit (2023) Optimal control of conveyor-mode spin-qubit shuttling in a Si/SiGe quantum bus in the presence of charged defectsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Ermoneit_2023_Optimal_control_of_conveyor-mode_spin-qubit_shuttling_in_a_Si_SiGe_quantum_bus_in_the_presence_of_charged_defects

belongs to
Publication c
has facts
doi I D ap W I A S. P R E P R I N T.3082 ep

Euler Backward Methodni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EulerBackwardMethod

similar to the (standard, forward, explicit) Euler method, but differs in that it is an implicit method. The backward Euler method has error of order one in time.
belongs to
Mathematical Formulation c
has facts
contains quantity op Time Step ni
generalizes formulation op Darcy Equation (Euler Backward) ni
generalizes formulation op Stokes Equation (Euler Backward) ni
defining formulation dp "$y_{n+1}=y_{n}+h f\left(t_{n+1}, y_{n+1}\right)$"^^La Te X ep
in defining formulation dp "$f$, function occuring on the right-hand-side of the ODE or PDE under consideration"^^La Te X ep
in defining formulation dp "$h$, Time Step"^^La Te X ep
in defining formulation dp "$h$, size of time step"^^La Te X ep
in defining formulation dp "$n$, index of time step"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$y$, function solving the ODE or PDE under consideration"^^La Te X ep
is time-continuous dp "false"^^boolean
description ap "In numerical analysis and scientific computing, this method is one of the most basic numerical methods for the solution of ordinary differential equations"@en
alt Label ap "Implicit Euler Method"
wikidata I D ap Q2736820 ep

Euler Forward Methodni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EulerForwardMethod

It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method.
belongs to
Mathematical Formulation c
has facts
contains quantity op Time ni
contains quantity op Time Step ni
defining formulation dp "$y_{n+1}=y_{n}+h f(t_n, y_n)$"^^La Te X ep
in defining formulation dp "$h$, Time Step"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
description ap "In mathematics and computational science, this method is a first-order numerical procedure for solving ODEs with a given initial value"@en
alt Label ap "Forward Euler Method"@en
wikidata I D ap Q868454 ep

Euler Numberni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#EulerNumber

mathematical constant; limit of (1 + 1/n)^n as n approaches infinity; transcendental number approximately equal 2.718281828....
belongs to
Quantity c
has facts
generalized by quantity op Real Number (Dimensionless) ni
description ap "mathematical constant"@en
wikidata I D ap Q82435 ep

Excess Substrate Assumptionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ExcessSubstrateAssumption

belongs to
Mathematical Formulation c
has facts
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains quantity op Enzyme Concentration ni
contains quantity op Substrate Concentration ni
defining formulation dp "$c_S >> c_E \rightarrow c_S \approx c_{S_{0}}$"^^La Te X ep
in defining formulation dp "$c_{E}$, Enzyme Concentration"^^La Te X ep
in defining formulation dp "$c_{S_{0}}$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$c_{S}$, Substrate Concentration"^^La Te X ep

Excitation Errorni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ExcitationError

belongs to
Quantity c
has facts
contained in formulation op Darwin-Howie-Whelan Equation for an unstrained crystal ni
contained in formulation op Darwin-Howie-Whelan Equation for a strained crystal ni
description ap "in dynamical electron scattering, the excitation error shows how well the Laue condition is satisfied"@en
doi I D ap s11082 020 02356 y ep

Expectation Valueni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ExpectationValue

belongs to
Quantity Kind c
has facts
generalizes quantity op Expectation Value (Quantum Density) ni
wikidata I D ap Q200125 ep

Expectation Value (Quantum Density)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ExpectationValueQuantumDensity

belongs to
Quantity c
has facts
defined by op Expectation Value (Quantum Density, Definition) ni
generalizes quantity op Expectation Value (Quantum State) ni
description ap "expected (mean) value of a quantum-mechanical observable, calculated from a density"@en
wikidata I D ap Q2918589 ep

Expectation Value (Quantum Density, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ExpectationValueQuantumDensityDefinition

belongs to
Mathematical Formulation c
has facts
contains quantity op Expectation Value (Quantum Density) ni
contains quantity op Quantum Density Operator ni
contains quantity op Quantum Mechanical Operator ni
defining formulation dp "$\langle \hat{O} \rangle \equiv \mathrm{tr}(\hat{O}\hat{\rho})$"^^La Te X ep
in defining formulation dp "$\hat{O}$, Quantum Mechanical Operator"^^La Te X ep
in defining formulation dp "$\langle \hat{O} \rangle$, Expectation Value (Quantum Density)"^^La Te X ep
in defining formulation dp "$\rho$, Quantum Density Operator"^^La Te X ep
description ap "expected (mean) value of a quantum-mechanical observable, calculated from a density"@en
wikidata I D ap Q2918589 ep

Expectation Value (Quantum State)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ExpectationValueQuantumState

belongs to
Quantity c
has facts
defined by op Expectation Value (Quantum State, Definition) ni
description ap "expected (mean) value of a quantum-mechanical observable, calculated from a density"@en

Expectation Value (Quantum State, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ExpectationValueQuantumStateDefinition

belongs to
Mathematical Formulation c
has facts
contains quantity op Expectation Value (Quantum State) ni
contains quantity op Quantum Mechanical Operator ni
contains quantity op Quantum State Vector ni
defining formulation dp "$\langle \hat{O} \rangle \equiv \langle \psi |\hat{O}| \psi \rangle$"^^La Te X ep
in defining formulation dp "$\hat{O}$, Quantum Mechanical Operator"^^La Te X ep
in defining formulation dp "$\langle \hat{O} \rangle$, Expectation Value (Quantum State)"^^La Te X ep
in defining formulation dp "$\psi$, Quantum State Vector"^^La Te X ep
description ap "expected (mean) value of a quantum-mechanical observable, calculated from a state vector"@en

Exposure Of An Individualni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ExposureOfAnIndividual

belongs to
Quantity c
has facts
generalized by quantity op Time ni
description ap "exposure (time) of an individual at a certain age"@en

External Chemical Potentialni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ExternalChemicalPotential

belongs to
Quantity c
has facts
description ap "chemical potential on the boundary of a domain, i.e., an interface"@en

External Force Densityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ExternalForceDensity

In fluid mechanics, the force density is the negative gradient of pressure. It has the physical dimensions of force per unit volume. Force density is a vector field representing the flux density of the hydrostatic force within the bulk of a fluid.
belongs to
Quantity c
has facts
description ap "vector field representing the flux density of the hydrostatic force within the bulk of a fluid"@en
wikidata I D ap Q4117184 ep

Extract Logical Rulesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ExtractLogicalRules

belongs to
Computational Task c
has facts
applies model op Object Comparison Model ni
contains formulation op Logical Rule Extraction Formulation ni
contains input op Boolean Ring ni
contains output op Gröbner Basis ni
description ap "extract logical rules underlying a boolean ring"@en

Extrinsic Mortalityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ExtrinsicMortality

belongs to
Quantity c
has facts
description ap "sum of the effects of external factors that contribute to death"@en
wikidata I D ap Q60776128 ep

Far Field Radiationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FarFieldRadiation

Shalva: Given ρ(r, t) and j(r, t) that are localized in some domain in space, calculate E(r, t) and B(r, t) far from this domain. For instance, calculate the electromagnetic field emitted by an oscillating dipole.
belongs to
Computational Task c
has facts
applies model op Maxwell Equations Model ni
description ap "electromagnetic radiation behaviors that predominate at greater distances"@en

Faraday Lawni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FaradayLaw

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Maxwell Equations Model ni
contains quantity op Electric Field ni
contains quantity op Magnetic Field ni
contains quantity op Time ni
defining formulation dp "$ \nabla \times \mathbf{E} &= -\frac{\partial \mathbf{B}} {\partial t}$"^^La Te X ep
in defining formulation dp "$B$, Magnetic Field"^^La Te X ep
in defining formulation dp "$E$, Electric Field"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
description ap "basic law of electromagnetism of magnetic fields inducing a potential difference"@en
alt Label ap "Faraday's law of induction"@en
wikidata I D ap Q181465 ep

Feedforward Neural Networkni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Feedforward_Neural_Network

belongs to
Mathematical Model c
has facts
generalized by op Artificial Neural Network ni
description ap "artificial neural network wherein connections between the nodes do not form a cycle"@en
wikidata I D ap Q5441227 ep

Fermi Potential For Electronsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FermiPotentialForElectrons

belongs to
Quantity c
has facts
contained in formulation op Poisson Equation For The Electric Potential ni
generalized by quantity op Energy ni
description ap "For use in semiconductor physics; strictly speaking, a quasi Fermi potential"@en
wikidata I D ap Q13633683 ep

Fermi Potential For Holesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FermiPotentialForHoles

belongs to
Quantity c
has facts
contained in formulation op Poisson Equation For The Electric Potential ni
generalized by quantity op Energy ni
description ap "For use in semiconductor physics; strictly speaking, a quasi Fermi potential"@en

Fiber Contraction Velocityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FibreContractionVelocity

belongs to
Quantity c
has facts
generalized by quantity op Velocity ni
description ap "speed at which muscle fibers change length during a contraction"@en

Fiber Stretchni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FibreStretch

belongs to
Quantity c
has facts
generalized by quantity op Linear Strain ni
description ap "stretch of a fibre, e.g. in a muscle"@en

Fick Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FickEquation

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
generalized by formulation op Classical Fokker Planck Equation ni
generalized by formulation op Transport Equation ni
defining formulation dp "$F = - \alpha \nabla u$"^^La Te X ep
in defining formulation dp "$F$, Diffusion Flux"^^La Te X ep
in defining formulation dp "$\alpha$, Diffusion Constant"^^La Te X ep
in defining formulation dp "$u$, Concentration"^^La Te X ep
description ap "mathematical description for transport of mass|particles by diffusion"@en
alt Label ap "Fick's law of diffusion"@en
wikidata I D ap Q856634 ep

Finite Volume Methodni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FiniteVolumeMethod

Finite volume methods can be compared and contrasted with the finite difference methods, which approximate derivatives using nodal values, or finite element methods, which create local approximations of a solution using local data, and construct a global approximation by stitching them together.
belongs to
Mathematical Formulation c
has facts
generalizes formulation op Continuity Equation For Electrons (Finite Volume) ni
generalizes formulation op Continuity Equation For Holes (Finite Volume) ni
generalizes formulation op Darcy Equation (Finite Volume) ni
generalizes formulation op Poisson Equation For The Electric Potential (Finite Volume) ni
generalizes formulation op Stokes Equation (Finite Volume) ni
is space-continuous dp "false"^^boolean
description ap "method for representing and evaluating partial differential equations in the form of algebraic equations"@en
wikidata I D ap Q1401936 ep

Fixed Costsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FixedCosts

belongs to
Quantity c
has facts
generalized by quantity op Costs ni
description ap "fixed costs for something, independend of e.g. time, length,..."@en
wikidata I D ap Q16897780 ep

Flow in porous mediani back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FlowInPorousMedia

belongs to
Research Problem c
has facts
contained in field op Continuum Mechanics ni
modeled by op Darcy Model ni
description ap "flow of an incompressible fluid through a porous medium"@en

Fluid Densityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FluidDensity

belongs to
Quantity c
has facts
generalized by quantity op Particle Number Density ni
description ap "measure of the mass per unit volume of a fluid"@en
alt Label ap "Fluid Mass Density"@en
wikidata I D ap Q101961654 ep

Fluid Dynamic Viscosity (Free Flow)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FluidDynamicViscosityFreeFlow

belongs to
Quantity c
has facts
generalized by quantity op Viscosity ni
description ap "physical property of a moving fluid in free flow"@en
wikidata I D ap Q15152757 ep

Fluid Dynamic Viscosity (Porous Medium)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FluidDynamicViscosityPorousMedium

belongs to
Quantity c
has facts
generalized by quantity op Viscosity ni
description ap "physical property of a moving fluid in a porous medium"@en
wikidata I D ap Q15152757 ep

Fluid Intrinsic Permeability (Porous Medium)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FluidIntrinsicPermeabilityPorousMedium

belongs to
Quantity c
has facts
description ap "measure of the ability of a porous material to allow fluids to pass through it"@en
alt Label ap "Intrinsic Permeability"@en

Fluid Kinematic Viscosity (Free Flow)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FluidKinematicViscosityFreeFlow

belongs to
Quantity c
has facts
generalized by quantity op Viscosity ni
description ap "characteristic of a fluid in free flow"@en
wikidata I D ap Q15106259 ep

Fluid Pressure (Free Flow)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FluidPressureFreeFlow

belongs to
Quantity c
has facts
generalized by quantity op Pressure ni
description ap "force exerted by a fluid (either a liquid or a gas) per unit area at any point within it in free flow"@en

Fluid Pressure (Porous Medium)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FluidPressurePorousMedium

belongs to
Quantity c
has facts
generalized by quantity op Pressure ni
description ap "force exerted by a fluid (either a liquid or a gas) per unit area at any point within it in porous medium"@en

Fluid Velocity (Free Flow)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FluidVelocityFreeFlow

belongs to
Quantity c
has facts
generalized by quantity op Velocity ni
description ap "vector field used to describe the motion of a fluid in a mathematical manner in free flow"@en
alt Label ap "Macroscopic Velocity (Free Flow)"@en

Fluid Velocity (Porous Medium)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FluidVelocityPorousMedium

belongs to
Quantity c
has facts
generalized by quantity op Velocity ni
description ap "vector field used to describe the motion of a fluid in a mathematical manner in porous medium"@en
alt Label ap "Macroscopic Velocity (Porous Medium)"@en

Fluid Viscous Stressni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FluidViscousStress

The viscous stress tensor models stress in continuum mechanics due to strain rate, representing material deformation at a point.
belongs to
Quantity c
has facts
description ap "models stress in continuum mechanics due to strain rate"@en
wikidata I D ap Q7935892 ep

Flux Of Electronsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FluxOfElectrons

For use in semiconductor physics
belongs to
Quantity c
has facts
contained in formulation op Continuity Equation For Electrons ni
contained in formulation op Current Density Of Electrons (Definition) ni
generalized by quantity op Particle Flux Density ni
description ap "flow of electrons, e.g., in an electric device"@en

Flux Of Holesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FluxOfHoles

For use in semiconductor physics
belongs to
Quantity c
has facts
contained in formulation op Continuity Equation For Holes ni
contained in formulation op Current Density Of Holes (Definition) ni
generalized by quantity op Particle Flux Density ni

Forceni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Force

physical influence that tends to cause an object to change motion unless opposed by other forces
belongs to
Quantity Kind c
has facts
qudt I D ap Force ep
wikidata I D ap Q11402 ep

Force Constant (Anharmonic)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ForceConstantAnharmonic

Cubic, quartic, ... anharmonic force constants are the coefficients of the third, fourth, ... order term in a Taylor expansion of the potential energy wrt displacements from a minimum energy configuration.
belongs to
Quantity c
has facts
generalizes quantity op Force Constant (Harmonic) ni
description ap "coefficients of the nth (n>=3) order term in a Taylor expansion of the potential energy wrt displacements from a minimum energy configuration"@en
wikidata I D ap Q545228 ep

Force Constant (Harmonic)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ForceConstantHarmonic

belongs to
Quantity c
is same as
Spring Constant ni
has facts
same As ep Spring Constant ni
description ap "coefficients of the second order term in a Taylor expansion of the potential energy wrt displacements from a minimum energy configuration"@en
wikidata I D ap Q170282 ep

Force Densityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ForceDensity

In fluid mechanics, the force density is the negative gradient of pressure. It has the physical dimensions of force per unit volume. Force density is a vector field representing the flux density of the hydrostatic force within the bulk of a fluid
belongs to
Quantity c
has facts
generalizes quantity op External Force Density ni
generalizes quantity op Surface Force Density ni
description ap "negative gradient of pressure"@en
wikidata I D ap Q4117184 ep

Fourier Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FourierEquation

Assuming that the local heat flux is equal to the product of thermal conductivity and the negative local temperature gradient
belongs to
Mathematical Formulation c
has facts
contains quantity op Temperature ni
generalized by formulation op Transport Equation ni
defining formulation dp "$q = - \gamma \nabla T$"^^La Te X ep
in defining formulation dp "$T$, Temperature"^^La Te X ep
in defining formulation dp "$\gamma$, Thermal Conductivity"^^La Te X ep
in defining formulation dp "$q$, Heat Flux"^^La Te X ep
description ap "differential form of Fourier's law of thermal conduction"@en
alt Label ap "Fourier's law of heat conduction"@en
wikidata I D ap Q12016821 ep

Fraction Of Population Density Of Exposedni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FractionOfPopulationDensityOfExposed

$e: \Omega \times [0, T] \rightarrow \mathbb{R}$ fraction of population density of exposed Individuals
belongs to
Quantity c
has facts
description ap "fraction of population density of exposed Individuals"@en

Fraction Of Population Density Of Exposed Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FractionOfPopulationDensityOfExposedFormulation

belongs to
Mathematical Formulation c
has facts
contained as formulation in op PDE SEIR Model ni
contains quantity op Density Fraction Coefficient ni
contains quantity op Fraction Of Population Density Of Exposed ni
contains quantity op Isotropic Gaussian Function ni
defining formulation dp "$e(x, 0)=\sum_{\tilde{l}=1}^{\tilde{L}} w_e^{(\tilde{l})} G^{(\tilde{l})}(x)$"^^La Te X ep
in defining formulation dp "$G^{(\tilde{l})}(x)$, Isotropic Gaussian Function"^^La Te X ep
in defining formulation dp "$e(x, 0)$, Fraction Of Population Density Of Exposed"^^La Te X ep
in defining formulation dp "$w_e^{(\tilde{l})} $, Density Fraction Coefficient"^^La Te X ep

Fraction Of Population Density Of Infectiousni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FractionOfPopulationDensityOfInfectious

$i: \Omega \times [0, T] \rightarrow \mathbb{R}$ fraction of population density of Infectious Individuals
belongs to
Quantity c
has facts
description ap "fraction of population density of Infectious Individuals"@en

Fraction Of Population Density Of Infectious Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FractionOfPopulationDensityOfInfectiousFormulation

belongs to
Mathematical Formulation c
has facts
contained as formulation in op PDE SEIR Model ni
contains quantity op Density Fraction Coefficient ni
contains quantity op Fraction Of Population Density Of Infectious ni
contains quantity op Isotropic Gaussian Function ni
defining formulation dp "$i(x, 0)=\sum_{\tilde{l}=1}^{\tilde{L}} w_i^{(\tilde{l})} G^{(\tilde{l})}(x)$"^^La Te X ep
in defining formulation dp "$G^{(\tilde{l})}(x)$, Isotropic Gaussian Function"^^La Te X ep
in defining formulation dp "$i(x, 0)$, Fraction Of Population Density of Infectious"^^La Te X ep
in defining formulation dp "$w_i^{(\tilde{l})} $, Density Fraction Coefficient"^^La Te X ep

Fraction Of Population Density Of Removedni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FractionOfPopulationDensityOfRemoved

$r: \Omega \times [0, T] \rightarrow \mathbb{R}$ fraction of population density of Removed Individuals
belongs to
Quantity c
has facts
description ap "fraction of population density of removed Individuals"@en

Fraction Of Population Density Of Susceptiblesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FractionOfPopulationDensityOfSusceptibles

$s: \Omega \times [0, T] \rightarrow \mathbb{R}$ fraction of population density of susceptible Individuals
belongs to
Quantity c
has facts
description ap "fraction of population density of susceptible Individuals"@en

Fraction Of Population Density Of Susceptibles Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FractionOfPopulationDensityOfSusceptiblesFormulation

belongs to
Mathematical Formulation c
has facts
contained as formulation in op PDE SEIR Model ni
contains quantity op Density Fraction Coefficient ni
contains quantity op Fraction Of Population Density Of Susceptibles ni
contains quantity op Isotropic Gaussian Function ni
defining formulation dp "$$ s(x, 0)=\sum_{\tilde{l}=1}^{\tilde{L}} w_s^{(\tilde{l})} G^{(\tilde{l})}(x)$$"^^La Te X ep
in defining formulation dp "$G^{(\tilde{l})}(x)$, Isotropic Gaussian Function"^^La Te X ep
in defining formulation dp "$s(x, 0)$, Fraction Of Population Density Of Susceptibles"^^La Te X ep
in defining formulation dp "$w_s^{(\tilde{l})} $, Density Fraction Coefficient"^^La Te X ep

Free Energy Densityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeEnergyDensity

belongs to
Quantity c
has facts
description ap "measure of the increase in the Helmholtz free energy per unit volume due to distortions"@en
wikidata I D ap Q865821 ep

Free Fall Determine Gravitationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallDetermineGravitation

belongs to
Computational Task c
has facts
applies model op Free Fall Model (Vacuum) ni
contains input op Free Fall Impact Time ni
contains input op Free Fall Initial Height ni
contains input op Free Fall Initial Velocity ni
contains output op Gravitational Acceleration (Earth Surface) ni
description ap "given the time that it takes for an object to freely fall from a certain height to the ground, what is the magnitude of the gravitational acceleration"@en

Free Fall Determine Timeni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallDetermineTime

how long does it take for a freely falling object to fall to the ground
belongs to
Computational Task c
has facts
applies model op Free Fall Model (Air Drag) ni
applies model op Free Fall Model (Vacuum) ni
contains assumption op Uniform Gravitational Acceleration ni
contains constant op Gravitational Acceleration (Earth Surface) ni
contains input op Free Fall Initial Height ni
contains input op Free Fall Initial Velocity ni
contains output op Free Fall Impact Time ni

Free Fall Determine Velocityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallDetermineVelocity

with which velocity will a freely falling object hit the ground
belongs to
Computational Task c
has facts
applies model op Free Fall Model (Air Drag) ni
applies model op Free Fall Model (Vacuum) ni
contains constant op Gravitational Acceleration (Earth Surface) ni
contains input op Free Fall Initial Height ni
contains input op Free Fall Initial Velocity ni
contains output op Free Fall Impact Velocity ni

Free Fall Equation (Air Drag)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallEquationAirDrag

Moreover, assuming the falling object to be a point mass.
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Free Fall Model (Air Drag) ni
contains quantity op Cross Section ni
contains quantity op Density Of Air ni
contains quantity op Drag Coefficient ni
contains quantity op Free Fall Height ni
contains quantity op Free Fall Initial Height ni
contains quantity op Free Fall Initial Velocity ni
contains quantity op Free Fall Mass ni
contains quantity op Free Fall Terminal Velocity ni
contains quantity op Free Fall Velocity ni
contains quantity op Gravitational Acceleration (Earth Surface) ni
contains quantity op Time ni
defining formulation dp "$\begin{align} m\dot{v} &=& mg-\frac{1}{2}\rho C_DAv^2\\ v(t) &=& v_{\infty}\tanh\left(\frac{gt}{v_{\infty}}\right) \\ y(t) &=& y_0+v_0t-\frac{v_\infty^2}{g}\ln\cosh\left(\frac{gt}{v_\infty}\right) \end{align}$"^^La Te X ep
in defining formulation dp "$A$, Cross Section"^^La Te X ep
in defining formulation dp "$C_D$, Drag Coefficient"^^La Te X ep
in defining formulation dp "$\rho$, Density of Air"^^La Te X ep
in defining formulation dp "$g$, Gravitational Acceleration (Earth Surface)"^^La Te X ep
in defining formulation dp "$m$, Free Fall Mass"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$v$, Free Fall Velocity"^^La Te X ep
in defining formulation dp "$v_0$, Free Fall Initial Velocity"^^La Te X ep
in defining formulation dp "$v_{\infty}$, Free Fall Terminal Velocity"^^La Te X ep
in defining formulation dp "$y$, Free Fall Height"^^La Te X ep
in defining formulation dp "$y_0$, Free Fall Initial Height"^^La Te X ep
is linear dp "false"^^boolean
description ap "modeling the fall of objects by the laws of classical mechanics, including aerodynamic drag and assuming a uniform gravitational field"@en
wikidata I D ap Q38083707 ep

Free Fall Equation (Non-Uniform Gravitation)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallEquationNonUniformGravitation

Moreover, assuming the falling object to be a point mass.
belongs to
Mathematical Formulation c
has facts
contains quantity op Free Fall Height ni
contains quantity op Free Fall Initial Height ni
contains quantity op Free Fall Time ni
generalizes formulation op Free Fall Equation (Vacuum) ni
defining formulation dp "y(t)=y_0~Q\left(1-\frac{t}{t_{\mathrm{ff}}};\frac{3}{2},\frac{1}{2}\right)"^^La Te X ep
in defining formulation dp "$t_\mathrm{ff}$, Free Fall Time"^^La Te X ep
in defining formulation dp "$y$, Free Fall Height"^^La Te X ep
in defining formulation dp "$y_0$, Free Fall Initial Height"^^La Te X ep
description ap "modeling the fall of objects by the laws of classical mechanics, neglecting aerodynamic drag but allowing for a non-uniform gravitational field"@en

Free Fall Equation (Vacuum)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallEquationVacuum

Moreover, assuming the falling object to be a point mass.
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Free Fall Model (Vacuum) ni
contains quantity op Free Fall Height ni
contains quantity op Free Fall Initial Height ni
contains quantity op Free Fall Initial Velocity ni
contains quantity op Free Fall Velocity ni
contains quantity op Gravitational Acceleration (Earth Surface) ni
contains quantity op Time ni
generalized by formulation op Free Fall Equation (Air Drag) ni
defining formulation dp "$\begin{align} \dot{v} &=& g \\ v(t) &=& v_0-gt \\ y(t) &=& y_0+v_0t-\frac{1}{2}gt^2 \end{align}$"^^La Te X ep
defining formulation dp "$v(t)=v_0-gt$"^^La Te X ep
defining formulation dp "$y(t)=y_0+v_0t-\frac{1}{2}gt^2$"^^La Te X ep
in defining formulation dp "$g$, Gravitational Acceleration (Earth Surface)"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$v$, Free Fall Velocity"^^La Te X ep
in defining formulation dp "$v_0$, Free Fall Initial Velocity"^^La Te X ep
in defining formulation dp "$y$, Free Fall Height"^^La Te X ep
in defining formulation dp "$y_0$, Free Fall Initial Height"^^La Te X ep
description ap "modeling the fall of objects by the laws of classical mechanics, neglecting aerodynamic drag and assuming a uniform gravitational field"@en
wikidata I D ap Q38083707 ep

Free Fall Heightni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallHeight

belongs to
Quantity c
has facts
generalized by quantity op Length ni
description ap "Height (altitude) of an object as it falls freely"@en
wikidata I D ap Q140028 ep

Free Fall Impact Timeni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallImpactTime

belongs to
Quantity c
has facts
generalized by quantity op Free Fall Time ni
description ap "time that it takes for an object to freely fall from a certain height to the ground"@en
wikidata I D ap Q5499609 ep

Free Fall Impact Velocityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallImpactVelocity

belongs to
Quantity c
has facts
description ap "velocity with which a freely falling object hits the ground"@en

Free Fall Initial Conditionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallInitialCondition

belongs to
Mathematical Formulation c
has facts
contained as initial condition in op Free Fall Equation (Air Drag) ni
contained as initial condition in op Free Fall Model (Vacuum) ni
contains quantity op Free Fall Height ni
contains quantity op Free Fall Initial Height ni
contains quantity op Free Fall Initial Velocity ni
contains quantity op Free Fall Velocity ni
contains quantity op Time ni
defining formulation dp "\begin{align} y(t=0) &= y_0 \\ v(t=0) &= v_0 \end{align}"^^La Te X ep
in defining formulation dp "$t$, time"^^La Te X ep
in defining formulation dp "$v$, Free Fall Velocity"^^La Te X ep
in defining formulation dp "$v_0$, Free Fall Initial Velocity"^^La Te X ep
in defining formulation dp "$y$, Free Fall Height"^^La Te X ep
in defining formulation dp "$y_0$, Free Fall Initial Height"^^La Te X ep
description ap "initial height and velocity of an object before it falls through a fluid or a gas"@en

Free Fall Initial Heightni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallInitialHeight

belongs to
Quantity c
has facts
defined by op Initial Classical Position ni
generalized by quantity op Free Fall Height ni
description ap "initial height (altitude) of an object as it starts falling through a fluid or a gas"@en

Free Fall Initial Velocityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallInitialVelocity

belongs to
Quantity c
has facts
defined by op Initial Classical Velocity ni
generalized by quantity op Free Fall Velocity ni
description ap "initial velocity of an object as it starts falling through a fluid or a gas"@en

Free Fall Massni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallMass

belongs to
Quantity c
has facts
generalized by quantity op Mass ni
description ap "Mass of a (freely) falling object"@en

Free Fall Model (Air Drag)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallModelAirDrag

belongs to
Mathematical Model c
has facts
models op Gravitational Effects On Fruit ni
description ap "mathematical model for the fall of objects, including the aerodynamic drag and assuming a uniform gravitational field"@en
wikidata I D ap Q38083707 ep

Free Fall Model (Non-Uniform Gravitation)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallModelNonUniformGravitation

belongs to
Mathematical Model c
has facts
contains formulation op Free Fall Equation (Non-Uniform Gravitation) ni
contains initial condition op Free Fall Initial Condition ni
generalizes model op Free Fall Model (Vacuum) ni
models op Gravitational Effects On Fruit ni
description ap "mathematical model for the fall of objects, including the aerodynamic drag and allowing for a non-uniform gravitational field"@en
wikidata I D ap Free fall ep

Free Fall Model (Vacuum)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallModelVacuum

A free fall is any motion of a body where gravity is the only force acting upon it. Hence, we are neglecting the aerodynamic drag (vanishing drag coefficient and/or density of air) and assuming a uniform gravitational field.
belongs to
Mathematical Model c
has facts
contains assumption op Uniform Gravitational Acceleration ni
contains assumption op Vanishing Air Density ni
contains assumption op Vanishing Drag Coefficient ni
generalized by model op Free Fall Model (Air Drag) ni
models op Gravitational Effects On Fruit ni
description ap "mathematical model for the fall of objects, neglecting aerodynamic drag and assuming a uniform gravitational field"@en
doi I D ap 012 ep
doi I D ap 1.3246467 ep
wikidata I D ap Q38083707 ep

Free Fall Terminal Velocityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallTerminalVelocity

belongs to
Quantity c
has facts
defined by op Free Fall Terminal Velocity (Definition) ni
generalized by quantity op Classical Velocity ni
generalized by quantity op Free Fall Velocity ni
description ap "highest velocity attainable by an object as it falls through a fluid or a gas"@en
wikidata I D ap Q614981 ep

Free Fall Terminal Velocity (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallTerminalVelocityDefinition

belongs to
Mathematical Formulation c
has facts
contains quantity op Cross Section ni
contains quantity op Density Of Air ni
contains quantity op Drag Coefficient ni
contains quantity op Free Fall Terminal Velocity ni
contains quantity op Gravitational Acceleration (Earth Surface) ni
contains quantity op Mass ni
defining formulation dp "$v_\infty \equiv \sqrt{\frac{2mg}{\rho C_D A}}$"^^La Te X ep
in defining formulation dp "$A$, Cross Section"^^La Te X ep
in defining formulation dp "$C_D$, Drag Coefficient"^^La Te X ep
in defining formulation dp "$\rho$, Density Of Air"^^La Te X ep
in defining formulation dp "$g$, Gravitational Acceleration (Earth Surface)"^^La Te X ep
in defining formulation dp "$m$, Mass"^^La Te X ep
in defining formulation dp "$v_\infty$, Free Fall Terminal Velocity"^^La Te X ep
description ap "highest velocity attainable by an object as it falls through a fluid or a gas"@en
wikidata I D ap Q614981 ep

Free Fall Timeni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallTime

belongs to
Quantity c
has facts
generalized by quantity op Time ni
description ap "characteristic time that would take a body to collapse under its own gravitational attraction, if no other forces existed to oppose the collapse"@en
wikidata I D ap Q5499609 ep

Free Fall Time (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallTimeDefinition

belongs to
Mathematical Formulation c
has facts
contains quantity op Earth Mass ni
contains quantity op Free Fall Height ni
contains quantity op Free Fall Initial Height ni
contains quantity op Free Fall Mass ni
contains quantity op Free Fall Time ni
contains quantity op Gravitational Constant ni
defines op Free Fall Time ni
defining formulation dp "t(y) \equiv \sqrt{ \frac{ {y_0}^3 }{2G(m+M)} } \left(\sqrt{\frac{y}{y_0}\left(1-\frac{y}{y_0}\right)} + \arccos{\sqrt{\frac{y}{y_0}}}\right)"^^La Te X ep
in defining formulation dp "$G$, Gravitational Constant"^^La Te X ep
in defining formulation dp "$M$, Earth Mass"^^La Te X ep
in defining formulation dp "$m$, Free Fall Mass"^^La Te X ep
in defining formulation dp "$t$, Free Fall Time"^^La Te X ep
in defining formulation dp "$y$, Free Fall Height"^^La Te X ep
in defining formulation dp "$y_0$, Free Fall Initial Height"^^La Te X ep
description ap "time of a freely falling object to reach the ground"@en
wikidata I D ap Q5499609 ep

Free Fall Velocityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFallVelocity

belongs to
Quantity c
has facts
generalized by quantity op Classical Velocity ni
generalizes quantity op Free Fall Terminal Velocity ni
description ap "velocity attained by an object as it falls freely"@en
wikidata I D ap Q140028 ep

Free flow coupled to porous media flowni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFlowCoupledToPorousMediaFlow

belongs to
Research Problem c
has facts
contained in field op Continuum Mechanics ni
modeled by op Stokes Darcy Model ni
description ap "coupled systems of free flow of an incompressible fluid adjacent to a permeable media"@en

Free flow of an incompressible fluidni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FreeFlowIncompressibleFluid

belongs to
Research Problem c
has facts
contained in field op Continuum Mechanics ni
modeled by op Stokes Model ni
description ap "free flow of an incompressible fluid (e.g. gas or liquid)"@en

Frequencyni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Frequency

Number of occurrences or cycles per time
belongs to
Quantity Kind c
has facts
qudt I D ap Frequency ep
wikidata I D ap Q11652 ep

Friction Coefficientni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#FrictionCoefficient

coefficient of friction, aka damping constant. Units of inverse time
belongs to
Quantity c
has facts
description ap "measure that quantifies the amount of friction existing between two surfaces"@en
alt Label ap "Damping Constant"@en
wikidata I D ap Q82580 ep

Gamma-Gompertz-Makeham Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GammaGompertzMakehamModel

We assume that death counts at age x are Poisson-distributed and the underlying population level hazard function follows a Gamma-Gompertz-Makeham model.
belongs to
Mathematical Model c
has facts
description ap "mathematical model for the mortality based on a Gamma-Gompertz-Makeham law"@en
wikidata I D ap Q2734378 ep

Gamma-Gompertz–Makeham Lawni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GammaGompertzMakehamLaw

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Gamma-Gompertz-Makeham Model ni
contains quantity op Age Of An Individual ni
contains quantity op Extrinsic Mortality ni
contains quantity op Heterogeneity of Death Rate ni
contains quantity op Level Of Mortality ni
contains quantity op Rate Of Aging ni
contains quantity op Risk Of Death ni
generalized by formulation op Gompertz–Makeham Law ni
defining formulation dp "$\mu(x) = \frac{a\exp(bx)}{1+\frac{a\gamma}{b}(\exp(bx)-1)}+c$"^^La Te X ep
in defining formulation dp "$\gamma$, Heterogeneity of Death Rate"^^La Te X ep
in defining formulation dp "$\mu$, Risk Of Death"^^La Te X ep
in defining formulation dp "$a$, Level of Mortality"^^La Te X ep
in defining formulation dp "$b$, Rate Of Aging"^^La Te X ep
in defining formulation dp "$c$, Extrinsic Mortality"^^La Te X ep
in defining formulation dp "$x$, Age Of An Individual"^^La Te X ep
description ap "mathematical formulation for the mortality based on a Gamma-Gompertz-Makeham law"@en
doi I D ap journal.pone.0198485 ep

Gated Recurrent Unit Layerni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GatedRecurrentUnitLayer

belongs to
Mathematical Formulation c
has facts
defining formulation dp "$\begin{align*} h_i &= z_i \cdot h_{i-1} + (1-z_i) \cdot \hat{h_i} \\ \hat{h_i} &= \tanh(W_h x_i + r_i \cdot U_h h_{i-1} + b_h) \\ z_i &= \sigma(W_z x_i + U_z h_{i-1} + b_z) \\ r_i &= \sigma(W_r x_i + U_r h_{i-1} +b_r) \\ \end{align*}&"^^La Te X ep
in defining formulation dp "$W$, weight matrix"^^La Te X ep
in defining formulation dp "$\hat{h_i}$,intermediate memory unit"^^La Te X ep
in defining formulation dp "$b$, bias"^^La Te X ep
in defining formulation dp "$h_i$,hidden layer"^^La Te X ep
in defining formulation dp "$r_i$, reset gate"^^La Te X ep
in defining formulation dp "$z_i$, update gate"^^La Te X ep
description ap "layer for recurrent neural network"@en

Gattermann (2017) Line pool generationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Gattermann_2017_Line_pool_generation

belongs to
Publication c
has facts
doi I D ap s12469 016 0127 x ep

Gauss Law (Electric Field)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GaussLawElectricField

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Maxwell Equations Model ni
contains quantity op Electric Charge Density ni
contains quantity op Electric Field ni
contains quantity op Permittivity (Vacuum) ni
generalizes formulation op Laplace Equation For The Electric Potential ni
generalizes formulation op Poisson Equation For The Electric Potential ni
defining formulation dp "$\nabla\cdot E=\frac{\rho}{\epsilon_0}$"^^La Te X ep
in defining formulation dp "$E$, Electric Field"^^La Te X ep
in defining formulation dp "$\epsilon_0$, Permittivity (Vacuum)"^^La Te X ep
in defining formulation dp "$\rho$, Electric Charge Density"^^La Te X ep
description ap "foundational law of electromagnetism stating that electric charges are the "sources" (divergence) of electric fields"@en
wikidata I D ap Q173356 ep

Gauss Law (Magnetic Field)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GaussLawMagneticField

Equivalently, magnetic monopoles do not exist
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Maxwell Equations Model ni
contains quantity op Magnetic Field ni
defining formulation dp "$\nabla\cdot B=0$"^^La Te X ep
in defining formulation dp "$B$, Magnetic Field"^^La Te X ep
description ap "foundational law of electromagnetism stating that the magnetic field B has divergence equal to zero"@en
wikidata I D ap Q1195250 ep

Gaussian Distributionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GaussianDistribution

belongs to
Quantity c
has facts
generalized by quantity op Probability Distribution ni
description ap "continuous probability distribution that is symmetric and bell-shaped"@en
alt Label ap "Normal Distribution"@en

Gaussian Distribution (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GaussianDistributionDefinition

belongs to
Mathematical Formulation c
has facts
contains quantity op Euler Number ni
contains quantity op Expectation Value ni
contains quantity op Gaussian Distribution ni
contains quantity op Pi Number ni
contains quantity op Variance ni
defines op Gaussian Distribution ni
defining formulation dp "$\varphi(z) \equiv \frac 1 {\sigma\sqrt{2\pi}} e^{ -(z-\mu)^2/(2\sigma^2) }$"^^La Te X ep
in defining formulation dp "$\mu$, Expectation Value"^^La Te X ep
in defining formulation dp "$\pi$, Pi Number"^^La Te X ep
in defining formulation dp "$\sigma$, Variance"^^La Te X ep
in defining formulation dp "$\varphi$, Gaussian Distribution"^^La Te X ep
in defining formulation dp "$e$, Euler Number"^^La Te X ep
description ap "continuous probability distribution that is symmetric and bell-shaped"@en
wikidata I D ap Q2725903 ep

Gaussian Noise Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GaussianNoiseModel

A typical model of image noise is Gaussian, additive, independent at each pixel, and independent of the signal intensity, caused primarily by Johnson–Nyquist noise (thermal noise), including that which comes from the reset noise of capacitors ("kTC noise").
belongs to
Mathematical Model c
has facts
contains formulation op Gaussian Distribution (Definition) ni
description ap "signal noise that has a probability density function equal to that of the normal distribution"@en
alt Label ap "Electronic Noise Model"@en
wikidata I D ap Q2725903 ep

Generic Product Identifierni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GenericProductIdentifier

The Generic Product Identifier (GPI) is a 14-character hierarchical classification system developed by Wolters Kluwer’s Medi-Span to identify drugs from their primary therapeutic use down to the unique interchangeable product, regardless of manufacturer or package size.
belongs to
Quantity c
has facts
description ap "14-character hierarchical classification system to identify drugs"@en
wikidata I D ap Q17033016 ep

Gompertz Lawni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GompertzLaw

Often applied to describe the distribution of adult lifespans by demographers.
belongs to
Mathematical Formulation c
has facts
description ap "in probability and statistics, the Gompertz distribution is a continuous probability distribution"@en
wikidata I D ap Q1011784 ep

Gompertz–Makeham Lawni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GompertzMakehamLaw

Note that the age-dependent component increases exponentially with age
belongs to
Mathematical Formulation c
has facts
generalized by formulation op Gompertz Law ni
description ap "mathematical equation describing the human death rate as a sum of an age-dependent component, and an age-independent component"@en
wikidata I D ap Q2734378 ep

Gramian Generalized Controllabilityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GramianGeneralizedControllability

belongs to
Quantity c
has facts
defined by op Gramian Generalized Controllability (Definition) ni
generalized by quantity op Gramian Matrix Observability ni
description ap "generalized Gramian of controllability, for use in bi-linear control problems"@en

Gramian Generalized Controllability (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GramianGeneralizedControllabilityDefinition

belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Matrix A ni
contains quantity op Control System Matrix B ni
contains quantity op Control System Matrix N ni
contains quantity op Gramian Generalized Controllability ni
contains quantity op Time ni
defining formulation dp "$\begin{align} W_c &=& \sum_{j=1}^{\infty} \int_0^\infty\ldots\int_0^\infty P_{j}(t_{1},\ldots t_{j}) P^{*}_{j}(t_{1}, \ldots t_{j}) \mathrm{d} t_{1} \ldots \mathrm{d} t_{j} \\ P_{1}(t_{1}) &=& e^{A t_{1}}iB \\ P_{j}(t_{1},\ldots,t_{j}) &=& e^{At_{j}}iN P_{j-1} \end{align}$"^^La Te X ep
in defining formulation dp "$A$, Control System Matrix A"^^La Te X ep
in defining formulation dp "$B$, Control System Matrix B"^^La Te X ep
in defining formulation dp "$N$, Control System Matrix N"^^La Te X ep
in defining formulation dp "$W_c$, Gramian Generalized Controllability"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
description ap "generalized Gramian of controllability, for use in bi-linear control problems"@en

Gramian Generalized Observabilityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GramianGeneralizedObservability

belongs to
Quantity c
has facts
defined by op Gramian Generalized Observability (Definition) ni
generalized by quantity op Gramian Matrix Observability ni
description ap "generalized Gramian of observability, for use in bi-linear control problems"@en

Gramian Generalized Observability (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GramianGeneralizedObservabilityDefinition

belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Matrix A ni
contains quantity op Control System Matrix C ni
contains quantity op Control System Matrix N ni
contains quantity op Gramian Generalized Observability ni
contains quantity op Time ni
defining formulation dp "$\begin{align} W_c &=& \sum_{j=1}^{\infty} \int_0^\infty\ldots\int_0^\infty Q^{*}_{j}(t_{1},\ldots t_{j})Q_{j}(t_{1},\ldots t_{j})\mathrm{d} t_{1}\ldots\mathrm{d} t_{j} \\ Q_{1}(t_{1}) &=& C e^{A^{*} t_{1}} \\ Q_{j}(t_{1},\ldots,t_{j}) X&=& Q_{j-1}iN e^{A^{*}t_{j}} \end{align}$"^^La Te X ep
in defining formulation dp "$A$, Control System Matrix A"^^La Te X ep
in defining formulation dp "$C$, Control System Matrix C"^^La Te X ep
in defining formulation dp "$N$, Control System Matrix N"^^La Te X ep
in defining formulation dp "$W_o$, Gramian Generalized Observability"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
description ap "generalized Gramian of observability, for use in bi-linear control problems"@en

Gramian Matrixni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GramianMatrix

belongs to
Quantity c
has facts
generalizes quantity op Gramian Matrix Controllability ni
generalizes quantity op Gramian Matrix Observability ni
description ap "matrix of inner products of a set of vectors"@en
wikidata I D ap Q1409400 ep

Gramian Matrix Controllabilityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GramianMatrixControllability

belongs to
Quantity c
has facts
contained in formulation op Lyapunov Equation Controllability ni
defined by op Gramian Matrix Controllability (Definition) ni
description ap "matrix used in linear control problems to determine whether a system is controllable"@en

Gramian Matrix Controllability (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GramianMatrixControllabilityDefinition

belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Matrix A ni
contains quantity op Control System Matrix B ni
contains quantity op Gramian Matrix Controllability ni
defining formulation dp "$W_c \& \equiv \int_0^\infty e^{At}iB(-i)B^* e^{A^*t}\mathrm{d} t$"^^La Te X ep
in defining formulation dp "$A$, Control System Matrix A"^^La Te X ep
in defining formulation dp "$B$, Control System Matrix B"^^La Te X ep
in defining formulation dp "$W_c$, Gramian Matrix Controllability"^^La Te X ep
description ap "matrix used in linear control problems to determine if a system is controllable"@en

Gramian Matrix Observabilityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GramianMatrixObservability

belongs to
Quantity c
has facts
contained in formulation op Lyapunov Equation Observability ni
defined by op Gramian Matrix Observability (Definition) ni
description ap "matrix used in linear control problems to determine whether a system is observable"@en

Gramian Matrix Observability (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GramianMatrixObservabilityDefinition

belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Matrix A ni
contains quantity op Control System Matrix C ni
contains quantity op Gramian Matrix Observability ni
defining formulation dp "$W_o \& \equiv \int_0^\infty e^{A^*t}C^*C e^{At}\mathrm{d} t$"^^La Te X ep
in defining formulation dp "$A$, Control System Matrix A"^^La Te X ep
in defining formulation dp "$C$, Control System Matrix C"^^La Te X ep
in defining formulation dp "$W_o$, Gramian Matrix Observability"^^La Te X ep
description ap "matrix used in linear control problems to determine if a system is observable"@en

Graph Type Identifierni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GraphTypeIdentifier

belongs to
Quantity c
has facts
contained in formulation op Line Costs Computation ni
description ap "variable identifying a graph as directed (value=1) or undirected (value=2)"@en

Gravitational Acceleration (Earth Surface)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GravitationalAccelerationEarthSurface

At a fixed point on the surface of Earth, the gravity results from the combined effect of gravitation and the centrifugal force from Earth's rotation. At different points on Earth's surface, the free fall acceleration ranges from 9.764 to 9.834 m/s2.
belongs to
Quantity c
has facts
generalized by quantity op Acceleration ni
description ap "acceleration of an object in free fall within a vacuum, thus without experiencing drag"@en
qudt I D ap Acceleration Of Gravity ep
wikidata I D ap Q30006 ep

Gravitational Acceleration (Earth Surface, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GravitationalAccelerationDefinition

belongs to
Mathematical Formulation c
has facts
contains quantity op Earth Mass ni
contains quantity op Earth Radius ni
contains quantity op Gravitational Acceleration (Earth Surface) ni
contains quantity op Gravitational Constant ni
defines op Gravitational Acceleration (Earth Surface) ni
defining formulation dp "$\vec{g} \equiv -\frac{GM}{r^2}\vec{r}$"^^La Te X ep
in defining formulation dp "$G$, Gravitational Constant"^^La Te X ep
in defining formulation dp "$M$, Earth Mass"^^La Te X ep
in defining formulation dp "$g$, Gravitational Acceleration (Earth Surface)"^^La Te X ep
in defining formulation dp "$r$, Earth Radius"^^La Te X ep
description ap "acceleration of an object in free fall within a vacuum, thus without experiencing drag"@en
qudt I D ap Standard Acceleration Of Gravity ep
wikidata I D ap Q30006 ep

Gravitational Constantni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GravitationalConstant

belongs to
Quantity c
has facts
description ap "physical constant relating the gravitational force between objects to their mass and distance"@en
qudt I D ap Gravitational Constant ep
wikidata I D ap Q18373 ep

Gravitational Effects On Fruitni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GravitationalEffectsOnFruit

belongs to
Research Problem c
has facts
contained in field op Classical Mechanics ni
contained in field op Pomology ni
modeled by op Free Fall Model (Vacuum) ni
description ap "studying how fruits are falling from trees, which inspired Newton of gravitation"@en

Gröbner Basisni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#GroebnerBasis

belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
description ap "particular generating subset of an ideal in a polynomial ring"@en
wikidata I D ap Q1551631 ep

H2 Optimal Approximationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#H2OptimalApproximation

This approach is based on the interpolation of the Volterra series representation of the system's transfer function and gives a local H2-optimal approximation, because the interpolation is chosen so that the system satisfies the necessary H2-optimality conditions upon convergence of the algorithm. Note that H2 stands for Hardy space
belongs to
Computational Task c
has facts
applies model op Control System Model ni
description ap "model order reduction by interpolation of the Volterra series representation of the system's transfer function"@en
doi I D ap j.cpc.2018.02.022 ep
doi I D ap 110836742 ep
doi I D ap jcd.2020001 ep

Hanes (1932) Studies on plant amylases: The effect of starch concentration upon the velocity of hydrolysis by the amylase of germinated barleyni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Hanes_1932_Studies_on_plant_amylases_The_effect_of_starch_concentration_upon_the_velocity_of_hydrolysis_by_the_amylase_of_germinated_barley

belongs to
Publication c
has facts
invents op Uni Uni Reaction (Hanes Woolf Model without Product - Irreversibility Assumption) ni
invents op Uni Uni Reaction (Hanes Woolf Model without Product - Rapid Equilibrium Assumption) ni
invents op Uni Uni Reaction (Hanes Woolf Model without Product - Steady State Assumption) ni
doi I D ap bj0261406 ep

Hanes Woolf Equation (Uni Uni Reaction without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#HanesWoolfEquationforUniUniReactionwithoutProductSteadyStateAssumption

Hanes Woolf Equation for Uni Uni Reaction without Product following Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product - Steady State Assumption) ni
defining formulation dp "$\frac{c_S}{v_0} = \frac{1}{V_{max,f}} * c_S + \frac{K_S}{V_{max,f}}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Hanes Woolf Equation (Uni Uni Reaction without Product - Irreversibility Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#HanesWoolfEquationforUniUniReactionwithoutProductIrreversibilityAssumption

Hanes Woolf Equation for Uni Uni Reaction without Product following Irreversibility Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Irreversibility Assumption) ni
contains quantity op Substrate Concentration ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product - Irreversibility Assumption) ni
defining formulation dp "$\frac{c_S}{v_0} = \frac{1}{V_{max,f}} * c_S + \frac{K_S}{V_{max,f}}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Irreversibility Assumption)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Hanes Woolf Equation (Uni Uni Reaction without Product - Rapid Equilibrium Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#HanesWoolfEquationforUniUniReactionwithoutProductRapidEquilibriumAssumption

Hanes Woolf Equation for Uni Uni Reaction without Product following Rapid Equilibrium Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Rapid Equilibrium Assumption) ni
contains quantity op Substrate Concentration ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product - Rapid Equilibrium Assumption) ni
defining formulation dp "$\frac{c_S}{v_0} = \frac{1}{V_{max,f}} * c_S + \frac{K_S}{V_{max,f}}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Rapid Equilibrium Assumption)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Hanes Woolf Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#HanesWoolfEquationUniUniReactionwithoutProductandCompetitiveCompleteInhibitionSteadyStateAssumption

Hanes Woolf Equation for Uni Uni Reaction without Product and competitive complete Inhibition following Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption) ni
defining formulation dp "$\frac{c_S}{v_0} = \frac{c_S}{V_{max,f}} + \frac{K_S * (1 + \frac{c_I}{K_{ic}})}{V_{max,f}}$"^^La Te X ep
in defining formulation dp "$K_S$,Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{ic}$,Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$,Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$,Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$,Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$,Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Hanes Woolf Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#HanesWoolfEquationUniUniReactionwithoutProductandMixedCompleteInhibitionSteadyStateAssumption

Hanes Woolf Equation for Uni Uni Reaction without Product and mixed complete Inhibition following Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni
defining formulation dp "$$\frac{c_S}{v_0} = \frac{c_S * (1 + \frac{c_I}{K_{iu}})}{V_{max,f}} + \frac{K_m * (1 + \frac{c_I}{K_{ic}})}{V_{max,f}}$$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{ic}$, Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$K_{iu}$, Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$, Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Hanes Woolf Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#HanesWoolfEquationUniUniReactionwithoutProductandNonCompetitiveCompleteInhibitionSteadyStateAssumption

Hanes Woolf Equation for Uni Uni Reaction without Product and non-competitive complete Inhibition following Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption) ni
similar to formulation op Hanes Woolf Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni
defining formulation dp "$\frac{c_S}{v_0} = \frac{c_S * (1 + \frac{c_I}{K_{iu}})}{V_{max,f}} + \frac{K_m * (1 + \frac{c_I}{K_{ic}})}{V_{max,f}}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{ic}$, Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$K_{iu}$, Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$, Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Hanes Woolf Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#HanesWoolfEquationUniUniReactionwithoutProductandUncompetitiveCompleteInhibitionSteadyStateAssumption

Hanes Woolf Equation for Uni Uni Reaction without Product and uncompetitive complete Inhibition following Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption) ni
defining formulation dp "$\frac{c_S}{v_0} = \frac{c_S * (1 + \frac{c_I}{K_{iu}})}{V_{max,f}} + \frac{K_S}{V_{max,f}}$"^^La Te X ep
in defining formulation dp "$K_S$,Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{iu}$,Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$,Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$,Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$,Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$,Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Hankel Singular Valueni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#HankelSingularValue

In control theory, Hankel singular values, named after Hermann Hankel, are the basis for balanced model reduction, in which controllable and observable states are retained while the remaining states are discarded. The reduced model retains the important features of the original model.
belongs to
Quantity c
has facts
description ap "basis for balanced model reduction, in which controllable and observable states are retained while the remaining states are discarded"@en
wikidata I D ap Q5648530 ep

Heat Conduction Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#HeatConductionModel

belongs to
Mathematical Model c
has facts
contains formulation op Fourier Equation ni
models op Heat Transport ni
description ap "mathematical model for thermal conduction based on Fourier's law"@en

Heat Fluxni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#HeatFlux

belongs to
Quantity c
has facts
contained in formulation op Fourier Equation ni
description ap "heat transferred per area and time"@en
alt Label ap "Heat Flux Density"@en
wikidata I D ap Q1478382 ep

Heat Transportni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#HeatTransport

belongs to
Research Problem c
has facts
contained in field op Continuum Mechanics ni
description ap "transfer of heat can be classified into various mechanisms, such as thermal conduction, thermal convection, thermal radiation"@en

Helfmann (2023) Modelling opinion dynamics under the impact of influencer and media strategiesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Helfmann_2023_Modelling_opinion_dynamics_under_the_impact_of_influencer_and_media_strategies

belongs to
Publication c
has facts
documents op Opinion Model With Influencers And Media ni
documents op Partial Mean Field Opinion Model ni
doi I D ap "https://doi.org/10.1038/s41598-023-46187-9"

Heterogeneity of Death Rateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#HeterogeneityOfDeathRate

belongs to
Quantity c
has facts
description ap "shows the different level of susceptibility to dying"@en

Hill-Type Two-Muscle-One-Tendon Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Hill-Type_Two-Muscle-One-Tendon_Model

belongs to
Mathematical Model c
has facts
models op Muscle Movement ni
studied in op Homs-Pons (2024) Coupled simulations and parameter inversion for neural system and electrophysiological muscle models ni
is deterministic dp "true"^^boolean
is dynamic dp "true"^^boolean
is linear dp "true"^^boolean
is space-continuous dp "true"^^boolean
is time-continuous dp "true"^^boolean
description ap "mathematical model derived from the balancing forces at the muscle ends"@en
description ap "mathematical model to predict lumped passive and active muscle forces during movement on a macroscopic scale"@en
doi I D ap gamm.202370009 ep
wikidata I D ap Q10331394 ep

Hill-Type Two-Muscle-One-Tendon ODE Systemni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Hill-Type_Two-Muscle-One-Tendon_ODE_System

System of Ordinary Differential Equations describing passive and active muscle forces during movement on a macroscopic scale, derived by balancing the forces on the muscle ends.
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Hill-Type Two-Muscle-One-Tendon Model ni
contains quantity op Active Contractile Force ni
contains quantity op Displacement Muscle Tendon ni
contains quantity op Effective Mass (Spring-Mass System) ni
contains quantity op Passive Muscle Force ni
contains quantity op Passive Tendon Force ni
contains quantity op Time ni
defining formulation dp "$ \begin{align*} m_{1} \ddot{x}_{1} &= F_\text{PTE}(t) -F_{\text{ACE}1}(t) - F_{\text{PME}1}(t) \\ m_{2} \ddot{x}_{2} &= -F_\text{PTE}(t) + F_{\text{ACE}2}(t) - F_{\text{PME}2}(t) \end{align*}$"^^La Te X ep
in defining formulation dp "$F_{\text{ACE}}$, Active contractile force"^^La Te X ep
in defining formulation dp "$F_{\text{PME}}$, Passive Muscle Force"^^La Te X ep
in defining formulation dp "$F_{\text{PTE}}$, Passive Tendon Force"^^La Te X ep
in defining formulation dp "$m$, Effective Mass (Spring-Mass System)"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$x$, Displacement Muscle Tendon"^^La Te X ep
description ap "system of ordinary differential equations describing passive and active muscle forces"@en
wikidata I D ap gamm.202370009 ep
wikidata I D ap Q10331394 ep

Hofstee (1959) Non-inverted versus inverted plots in enzyme kineticsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Hofstee_1959_Non_inverted_versus_inverted_plots_in_enzyme_kinetics

belongs to
Publication c
has facts
invents op Uni Uni Reaction (Eadie Hofstee Model without Product - Irreversibility Assumption) ni
invents op Uni Uni Reaction (Eadie Hofstee Model without Product - Rapid Equilibrium Assumption) ni
invents op Uni Uni Reaction (Eadie Hofstee Model without Product - Steady State Assumption) ni
doi I D ap 1841296b0 ep

Homs-Pons (2024) Coupled simulations and parameter inversion for neural system and electrophysiological muscle modelsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Homs-Pons_2024_Coupled_simulations_and_parameter_inversion_for_neural_system_and_electrophysiological_muscle_models

belongs to
Publication c
has facts
doi I D ap gamm.202370009 ep

Hooke Law (Linear Elasticity)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#HookeLawLinearElasticity

An empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, $F = kx$. Also the stresses and strains of material inside a continuous elastic material are connected by a linear relationship that is mathematically similar to Hooke's spring law, and is often referred to by that name.
belongs to
Mathematical Formulation c
has facts
contains quantity op Displacement Of Atoms ni
contains quantity op Elastic Stiffness Tensor ni
contains quantity op Mechanical Strain ni
contains quantity op Mechanical Stress ni
defining formulation dp "$\sigma=C:\epsilon$where $\epsilon(u)=\frac{1}{2}(\nabla u+(\nabla u)^T)$"^^La Te X ep
in defining formulation dp "$C$, Elastic Stiffness Tensor"^^La Te X ep
in defining formulation dp "$\epsilon$, Mechanical Strain"^^La Te X ep
in defining formulation dp "$\sigma$, Mechanical Stress"^^La Te X ep
in defining formulation dp "$u$, Displacement of Atoms"^^La Te X ep
description ap "force to extend or compress a spring by distance scales linearly with distance"@en
wikidata I D ap Q1913277 ep
wikidata I D ap Q170282 ep

Hooke Law (Spring)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#HookLawSpring

An empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, $F = kx$, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring. The law is named after 17th-century British physicist Robert Hooke.
belongs to
Mathematical Formulation c
has facts
contains quantity op Change In Length ni
contains quantity op Force ni
contains quantity op Spring Constant ni
generalized by formulation op Hooke Law (Linear Elasticity) ni
defining formulation dp "$F = k \Delta l$"^^La Te X ep
in defining formulation dp "$F$, Force"^^La Te X ep
in defining formulation dp "$\Delta l$, Change In Length"^^La Te X ep
in defining formulation dp "$k$, Spring Constant"^^La Te X ep
description ap "force to extend or compress a spring by distance scales linearly with distance"@en
wikidata I D ap Q170282 ep

Hydraulic Conductivityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#HydraulicConductivity

belongs to
Quantity c
has facts
description ap "measure of the ability of a porous material to allow water to pass through it"@en
wikidata I D ap Q2783041 ep

Hyperstress Potentialni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#HyperstressPotential

belongs to
Quantity c
has facts
description ap "Hyperstress potential in calculations of elasticity"@en

Idealni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Ideal

belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
description ap "additive subgroup of a ring closed under multiplcation by arbitrary ring element"@en
wikidata I D ap Q44649 ep

Identify destruction rules in ancient egyptian objectsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#IdentifyDestructionRulesInAncientEgyptianObjects

common destruction patterns in ancient egyptian objects from the 'Cachette de Karnak' suggest that specific rules govern these occurences
belongs to
Research Problem c
has facts
contained in field op Egyptology ni

Image Denoisingni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ImageDenoising

belongs to
Research Problem c
has facts
contained in field op Medical Imaging ni
contained in field op Statistics ni
modeled by op Gaussian Noise Model ni
description ap "removal of noise from images."@en
wikidata I D ap Q108033749 ep

Imaging of nanostructuresni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ImagingOfNanostructures

(1) We present a mathematical model and a tool chain for the numerical simulation of transmission electron microscopy (TEM) images of semiconductor quantum dots (QDs). This includes elasticity theory to obtain the strain profile coupled with the Darwin–Howie–Whelan equations, describing the propagation of the electron wave through the sample.
belongs to
Research Problem c
has facts
contained in field op Transmission Electron Microscopy ni
modeled by op Dynamical Electron Scattering Model ni
description ap "mathematical model for transmission electron microscopy of nanostructures"@en
doi I D ap s11082 020 02356 y ep
wikidata I D ap Q110779037 ep

Individual Relationship Matrixni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#IndividualRelationshipMatrix

belongs to
Quantity c
has facts
description ap "relations among individuals such as friendship or connections on social media are defined through a binary adjacency matrix"@en

Inertia Parameter For Opinion Changes Of Influencersni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InfluencerInertiaParameter

The resistance to rapid opinion change is determined by the inertia parameter $\gamma > 1$ for Influencers.
belongs to
Quantity c
has facts
description ap "parameter indicating resistance to rapid optinion change of influencers"@en

Inertia Parameter For Opinion Changes Of Mediani back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MediaInertiaParameter

THe resistance to rapid opinion change is determined by the inertia parameter $\Gamma > 1$ for media agents
belongs to
Quantity c
has facts
description ap "parameter indicating resistance to rapid optinion change of media agents"@en

Infected Recovery Rateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InfectedRecoveryRate

belongs to
Quantity c
has facts
description ap "constant representing the infected recovery rate"@en

Infectiousni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Infectious

belongs to
Quantity c
has facts
generalized by quantity op Integer Number (Dimensionless) ni
generalizes quantity op Number Of Infectious Individuals ni
generalizes quantity op Number Of Infected Cities ni
is dimensionless dp "true"^^boolean
description ap "general quantity for the number of infectious entities"@en

Infectious At Time Step n+1 in the Multi-Population SI Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InfectiousAtTimeStepInTheMultiPopulationSIModel

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Multi-Population Discrete Susceptible Infectious Model ni
contains quantity op Contact Rate Between Two Groups ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time Step ni
contains quantity op Total Population Size ni
defining formulation dp "$I_{n+1}^i = I_n^i + S_n^i \sum_{k=1}^K\frac{\alpha_{ik} \Delta t}{N^i} I_n^k$"^^La Te X ep
in defining formulation dp "$I_n^i$, Infectious Individuals"^^La Te X ep
in defining formulation dp "$N^i$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_n^i$, Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha_{ik}$, Contact Rate Between Two Groups"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Infectious At Time Step n+1 in the Multi-Population SIR Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InfectiousAtTimeStepInTheMultiPopulationSIRModel

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Multi-Population Discrete Susceptible Infectious Removed Model ni
contains quantity op Contact Rate Between Two Groups ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Relative Removal Rate ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time Step ni
contains quantity op Total Population Size ni
defining formulation dp "$I_{n+1}^i = I_n^i \left(1 - \gamma_i \Delta t \right) +S_n^i \sum_{k=1}^K\frac{\alpha_{ik} \Delta t}{N^i} I_n^k$"^^La Te X ep
in defining formulation dp "$I_n^i$, Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_n^i$, Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha_{ik}$, Contact Rate Between Two Groups"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Infectious At Time Step n+1 in the Multi-Population SIS Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InfectiousAtTimeStepInTheMultiPopulationSISModel

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Multi-Population Discrete Susceptible Infectious Susceptible Model ni
contains quantity op Contact Rate Between Two Groups ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Relative Removal Rate ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time Step ni
contains quantity op Total Population Size ni
defining formulation dp "$S_{n+1}^i = S_n^i \left(1- \sum_{k=1}^K \frac{\alpha_{ik} \Delta t}{N^i} I_n^k\right) + \gamma_i \Delta t I_n^i$"^^La Te X ep
in defining formulation dp "$I_n^i$, Infectious Individuals"^^La Te X ep
in defining formulation dp "$N^i$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_n^i$, Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha_{ik}$, Contact Rate Between Two Groups"^^La Te X ep
in defining formulation dp "$\gamma_i$, Relative Removal Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Infectious At Time Step n+1 in the SI Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InfectiousAtTimeStepInTheSIModel

equation to define the number of infectious Individuals at time step (n+1)Δt in the SI Model
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Discrete Susceptible Infectious Model ni
contains quantity op Contact Rate ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time Step ni
contains quantity op Total Population Size ni
defining formulation dp "$I_{n+1}=I_n\left(1+\frac{\alpha \Delta t}{N} S_n\right)$"^^La Te X ep
in defining formulation dp "$I_n$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_n$, Number Of Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha$, Contact Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Infectious At Time Step n+1 in the SIR Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InfectiousAtTimeStepInTheSIRModel

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Discrete Susceptible Infectious Removed Model ni
contains quantity op Contact Rate ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Relative Removal Rate ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time Step ni
contains quantity op Total Population Size ni
discretizes op Continuous Rate of Change of Infectious in the SIR Model ni
defining formulation dp "$I_{n+1}=I_n\left(1 - \gamma \Delta t +\frac{\alpha \Delta t}{N} S_n\right)$"^^La Te X ep
in defining formulation dp "$I_n$, Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_n$, Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha$, Contact Rate"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Infectious At Time Step n+1 in the SIR Model with Births and Deathsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InfectiousAtTimeStepInTheSIRModelWithBirthsAndDeaths

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Susceptible Infectious Removed Model with Births and Deaths ni
contains quantity op Birth Rate ni
contains quantity op Contact Rate ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Relative Removal Rate ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time Step ni
contains quantity op Total Population Size ni
defining formulation dp "$I_{n+1}=I_n\left(1 - \gamma \Delta t - \beta \Delta t +\frac{\alpha \Delta t}{N} S_n\right)$"^^La Te X ep
in defining formulation dp "$I_n$, Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_n$, Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha$, Contact Rate"^^La Te X ep
in defining formulation dp "$\beta$, Birth Rate"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Infectious At Time Step n+1 in The SIS Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#infectiousAtTimeStepInTheSISModel

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Discrete Susceptible Infectious Susceptible Model ni
contains quantity op Contact Rate ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Relative Removal Rate ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time Step ni
contains quantity op Total Population Size ni
defining formulation dp "$I_{n+1}=I_n\left(1 - \gamma \Delta t +\frac{\alpha \Delta t}{N} S_n\right)$"^^La Te X ep
in defining formulation dp "$I_n$, Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_n$, Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha$, Contact Rate"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Infectious At Time Step n+1 in The SIS Model with births and deathsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InfectiousAtTimeStepInTheSISModelWithBirthsAndDEaths

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Susceptible Infectious Susceptible Model with Births and Deaths ni
contains quantity op Birth Rate ni
contains quantity op Contact Rate ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Relative Removal Rate ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time Step ni
contains quantity op Total Population Size ni
defining formulation dp "$S_{n+1}=S_n\left(1-\frac{\alpha \Delta t}{N} I_n\right) + \gamma \Delta t I_n + \beta \Delta t (N - S_n)$"^^La Te X ep
in defining formulation dp "$I_n$, Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_n$, Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha$, Contact Rate"^^La Te X ep
in defining formulation dp "$\beta$, Birth Rate"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Influencer Individual Matrixni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InfluencerIndividualMatrix

$\{0, 1\}^{L\times N}$ Binary adjacency Matrix which defines the connections between individuals and influencers at time t
belongs to
Quantity c
has facts
description ap "adjacency matrix defining the connections between individuals and influencers at time t"@en

Inhibition Constantni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstant

belongs to
Quantity c
has facts
generalized by quantity op Dissociation Constant ni

Inhibition Constant Product 1 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantProduct1BiBiReactionOrderedSingleCCSS

belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibition Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{iP_1} = \frac{k_5}{k_{-5}}$"^^La Te X ep
in defining formulation dp "$K_{iP_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$k_{-5}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{5}$, Reaction Rate Constant"^^La Te X ep

Inhibition Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantProduct1BiBiReactionOrderedSteadyStateAssumption

Inhibition constant for the product 1 of a Bi Bi Reaction with Ordered Mechanism under the Staedy State Assumption
belongs to
Quantity c
has facts
defined by op Inhibition Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption, Definition) ni
generalized by quantity op Concentration ni
generalized by quantity op Inhibition Constant ni
is dimensionless dp "false"^^boolean
description ap "chemical constant"@en

Inhibition Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantProduct1BiBiReactionOrderedSteadyStateAssumptionDefinition

Definition of Inhibition constant for the product 1 of a Bi Bi Reaction with Ordered Mechanism under the Staedy State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibition Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{iP_1} \equiv \frac{k_5}{k_{-5}}$"^^La Te X ep
in defining formulation dp "$K_{iP_1}$, Inhibition Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$k_{-5}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{5}$, Reaction Rate Constant"^^La Te X ep

Inhibition Constant Product 1 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantProduct1BiBiReactionPingPongSS

belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibition Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{iP_1} = \frac{k_{2}}{k_{-2}}$"^^La Te X ep
in defining formulation dp "$K_{iP_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep

Inhibition Constant Product 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantProduct1BiBiReactionTheorellChanceSS

belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibition Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{iP_1} = \frac{k_{3}}{k_{-2}}$"^^La Te X ep
in defining formulation dp "$K_{iP_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep

Inhibition Constant Product 2 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantProduct2BiBiReactionOrderedSingleCCSS

belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibition Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{iP_2} = \frac{k_4 + k_5}{k_{-4}}$"^^La Te X ep
in defining formulation dp "$K_{iP_2}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{5}$, Reaction Rate Constant"^^La Te X ep

Inhibition Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantProduct2BiBiReactionOrderedSteadyStateAssumption

Inhibition constant for the product 2 of a Bi Bi Reaction with Ordered Mechanism under the Staedy State Assumption
belongs to
Quantity c
has facts
defined by op Inhibition Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption, Definition) ni
generalized by quantity op Concentration ni
generalized by quantity op Inhibition Constant ni
is dimensionless dp "false"^^boolean
description ap "chemical constant"@en

Inhibition Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantProduct2BiBiReactionOrderedSteadyStateAssumptionDefinition

Definition of Inhibition constant for the product 2 of a Bi Bi Reaction with Ordered Mechanism under the Staedy State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibition Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{iP_2} \equiv \frac{k_4 * k_5 + k_3 * k_4 + k_3 * k_5 + k_{-3} * k_5}{k_{-4} * (k_3 + k_{-3})}$"^^La Te X ep
in defining formulation dp "$K_{iP_2}$, Inhibition Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{5}$, Reaction Rate Constant"^^La Te X ep

Inhibition Constant Product 2 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantProduct2BiBiReactionPingPongSS

belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibition Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{iP_2} = \frac{k_{4}}{k_{-4}}$"^^La Te X ep
in defining formulation dp "$K_{iP_2}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep

Inhibition Constant Product 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantProduct2BiBiReactionTheorellChanceSS

belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibition Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{iP_2} = \frac{k_{3}}{k_{-3}}$"^^La Te X ep
in defining formulation dp "$K_{iP_2}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep

Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantSubstrate1BiBiReactionOrderedSingleCCSS

belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibition Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{iS_1} = \frac{k_{-1}}{k_{1}}$"^^La Te X ep
in defining formulation dp "$K_{iS_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep

Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantSubstrate1BiBiReactionOrderedSteadyStateAssumption

Inhibition constant for the substrate 1 of a Bi Bi Reaction with Ordered Mechanism under the Staedy State Assumption
belongs to
Quantity c
has facts
defined by op Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption, Definition) ni
generalized by quantity op Dissociation Constant ni
generalized by quantity op Inhibition Constant ni
is dimensionless dp "false"^^boolean
description ap "chemical constant"@en

Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantSubstrate1BiBiReactionOrderedSteadyStateAssumptionDefinition

Definition of Inhibition constant for the substrate 1 of a Bi Bi Reaction with Ordered Mechanism under the Staedy State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{iS_1} \equiv \frac{k_{-1}}{k_{1}}$"^^La Te X ep
in defining formulation dp "$K_{iS_1}$, Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep

Inhibition Constant Substrate 1 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantSubstrate1BiBiReactionPingPongSS

belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibition Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{iS_1} = \frac{k_{-1}}{k_{1}}$"^^La Te X ep
in defining formulation dp "$K_{iS_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep

Inhibition Constant Substrate 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantSubstrate1BiBiReactionTheorellChanceSS

belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibition Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{iS_1} = \frac{k_{-1}}{k_{1}}$"^^La Te X ep
in defining formulation dp "$K_{iS_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep

Inhibition Constant Substrate 2 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantSubstrate2BiBiReactionOrderedSingleCCSS

belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibition Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{iS_2} = \frac{k_{-1} + k_{-2}}{k_2}$"^^La Te X ep
in defining formulation dp "$K_{iS_2}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep

Inhibition Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantSubstrate2BiBiReactionOrderedSteadyStateAssumption

Inhibition constant for the substrate 2 of a Bi Bi Reaction with Ordered Mechanism under the Staedy State Assumption
belongs to
Quantity c
has facts
defined by op Inhibition Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption, Definition) ni
generalized by quantity op Concentration ni
generalized by quantity op Inhibition Constant ni
is dimensionless dp "false"^^boolean
description ap "chemical constant"@en

Inhibition Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantSubstrate2BiBiReactionOrderedSteadyStateAssumptionDefinition

Definition of Inhibition constant for the substrate 2 of a Bi Bi Reaction with Ordered Mechanism under the Staedy State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibition Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{iS_2} \equiv \frac{k_{-1} * k_{-2} + k_{-1} * k_3 + k_{-1} * k_{-3} + k_{-2} * k_{-3}}{k_2 * (k_3 + k_{-3})}$"^^La Te X ep
in defining formulation dp "$K_{iS_2}$, Inhibition Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep

Inhibition Constant Substrate 2 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantSubstrate2BiBiReactionPingPongSS

belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibition Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{iS_2} = \frac{k_{-3}}{k_{3}}$"^^La Te X ep
in defining formulation dp "$K_{iS_2}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep

Inhibition Constant Substrate 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitionConstantSubstrate2BiBiReactionTheorellChanceSS

belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibition Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{iS_2} = \frac{k_{-1}}{k_{2}}$"^^La Te X ep
in defining formulation dp "$K_{iS_2}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep

Inhibitor Concentrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InhibitorConcentration

belongs to
Quantity c
has facts
generalized by quantity op Concentration ni
is dimensionless dp "false"^^boolean
description ap "amount of inhibitor present in a reaction environment"@en

Initial Classical Densityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialClassicalDensity

belongs to
Mathematical Formulation c
has facts
contained as initial condition in op Classical Dynamics Model ni
contains quantity op Classical Density (Phase Space) ni
contains quantity op Time ni
generalized by formulation op Initial Quantum Density ni
defining formulation dp "$\rho(t=0)=\rho_0$"^^La Te X ep
in defining formulation dp "$\rho$, Classical Density (Phase Space)"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
description ap "initial phase-space density distribution of a classical mechanical system"@en

Initial Classical Momentumni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialClassicalMomentum

belongs to
Mathematical Formulation c
has facts
contains quantity op Classical Momentum ni
contains quantity op Time ni
defining formulation dp "$p(t=0)=p_0$"^^La Te X ep
in defining formulation dp "$p$, Classical Momentum"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
description ap "initial momentum of a classical particle modeled as point mass"@en

Initial Classical Positionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialClassicalPosition

belongs to
Mathematical Formulation c
has facts
contains quantity op Classical Position ni
contains quantity op Time ni
defining formulation dp "$q(t=0)=q_0$"^^La Te X ep
in defining formulation dp "$q$, Classical Position"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
description ap "initial position of a classical particle modeled as point mass"@en

Initial Classical Velocityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialClassicalVelocity

initial velocity of a classical particle modeled as point mass
belongs to
Mathematical Formulation c
has facts
contains quantity op Classical Velocity ni
contains quantity op Time ni
defining formulation dp "$v(t=0)=v_0$"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$v$, Classical Velocity"^^La Te X ep

Initial Condition for the Multi-Population SI Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialConditionForTheMultiPopulationSIModel

for each subpopulation, the initial number of susceptibles + initial number of Infectious is equal to the Total population
belongs to
Mathematical Formulation c
has facts
contained as initial condition in op Multi-Population Discrete Susceptible Infectious Model ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Total Population Size ni
defining formulation dp "$S_0^i + I_0^i = N^i$"^^La Te X ep
in defining formulation dp "$I_0^i$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N^i$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_0^i$, Number Of Susceptible Individuals"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Initial Condition for the Multi-Population SIS Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialConditionForTheMultiPopulationSISModel

belongs to
Mathematical Formulation c
has facts
contained as initial condition in op Multi-Population Discrete Susceptible Infectious Susceptible Model ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Total Population Size ni
defining formulation dp "$S_0^i + I_0^i = N^i$"^^La Te X ep
in defining formulation dp "$I_0^i$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N^i$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_0^i$, Number Of Susceptible Individuals"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Initial Condition for the Continuous SI Model and SIS Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialConditionForTheContinuousSIModelAndSISModel

Initial condition to be satisfyied in case of the Continuous SI Model ans SIS Model
belongs to
Mathematical Formulation c
has facts
contained as initial condition in op Continuous Susceptible Infectious Model ni
contained as initial condition in op Continuous Susceptible Infectious Susceptible Model ni
contained as initial condition in op Discrete Susceptible Infectious Susceptible Model ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Total Population Size ni
discretized by formulation op Initial Condition for the Discrete SI Model ni
defining formulation dp "$S(0) + I(0) = N$"^^La Te X ep
in defining formulation dp "$I$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$S$, Number Of Susceptible Individuals"^^La Te X ep
is deterministic dp "true"^^boolean

Initial Condition for the Continuous SIR Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialConditionForTheContinuousSIRModel

Initial condition to be satisfied in case of the Continuous SIR Model
belongs to
Mathematical Formulation c
has facts
contained as initial condition in op Continuous Susceptible Infectious Removed Model ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Removed Individuals ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Total Population Size ni
defining formulation dp "$S(0) + I(0) + R(0) = N$"^^La Te X ep
in defining formulation dp "$I_0$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$R_0$, Number Of Removed Individuals"^^La Te X ep
in defining formulation dp "$S_0$, Number Of Susceptible Individuals"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean

Initial Condition for the Discrete SI Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialConditionForTheDiscreteSIModel

Initial condition to be satisfied in case of the discrete SI Model
belongs to
Mathematical Formulation c
has facts
contained as initial condition in op Discrete Susceptible Infectious Model ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Total Population Size ni
defining formulation dp "$S_0 + I_0 = N$"^^La Te X ep
in defining formulation dp "$I_0$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_0$, Number Of Susceptible Individuals"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Initial Condition For The Discrete SIR Model with and without Births and Deathsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialConditionForTheDiscreteSIRModel

Initial condition to be satisfied in case of the discrete SI Model
belongs to
Mathematical Formulation c
has facts
contained as initial condition in op Discrete Susceptible Infectious Removed Model ni
contained as initial condition in op Susceptible Infectious Removed Model with Births and Deaths ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Removed Individuals ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Total Population Size ni
discretizes op Initial Condition for the Continuous SIR Model ni
defining formulation dp "$S_0 + I_0 + R_0 = N$"^^La Te X ep
in defining formulation dp "$I_0$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$R_0$, Number Of Removed Individuals"^^La Te X ep
in defining formulation dp "$S_0$, Number Of Susceptible Individuals"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Initial Condition for the Multi-Population SIR Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialConditionForTheMultiPopulationSIRModel

for each subpopulation, the initial number of susceptibles, Infectious and Removed, combined, is equal to the Total population
belongs to
Mathematical Formulation c
has facts
contained as initial condition in op Multi-Population Discrete Susceptible Infectious Removed Model ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Removed Individuals ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Total Population Size ni
defining formulation dp "$S_0^i + I_0^i + R_0^i = N^i$"^^La Te X ep
in defining formulation dp "$I_n$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$R_n$, Number Of Removed Individuals"^^La Te X ep
in defining formulation dp "$S_n$, Number Of Susceptible Individuals"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Initial Control Stateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialControlState

belongs to
Mathematical Formulation c
has facts
contained as initial condition in op Control System Model (Linear) ni
contains quantity op Control System Initial ni
contains quantity op Control System State ni
contains quantity op Time ni
defines op Control System Initial ni
defining formulation dp "$x(t=0)=x_0$"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$x$, Control System State"^^La Te X ep
in defining formulation dp "$x_0$, Control System Initial"^^La Te X ep
description ap "initial state of a control system"@en

Initial Control State (Reduced)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialControlStateReduced

belongs to
Quantity c
has facts
contained as input in op Balanced Truncation (Bi-linear) ni
contained as input in op Balanced Truncation (Linear) ni
contained as input in op H2 Optimal Approximation (Bi-linear) ni
contained as input in op H2 Optimal Approximation (Linear) ni
defined by op Initial Control State (Reduced, Definition) ni
description ap "initial state of a control system; after model order reduction"@en

Initial Control State (Reduced, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialControlStateReducedDefinition

belongs to
Mathematical Formulation c
has facts
contains quantity op Control System State (Reduced) ni
contains quantity op Initial Control State (Reduced) ni
contains quantity op Time ni
defines op Initial Control State (Reduced) ni
defining formulation dp "$\tilde{x}(t=0) \equiv \tilde{x}_0$"^^La Te X ep
in defining formulation dp "$\tilde{x}$, Control System State (Reduced)"^^La Te X ep
in defining formulation dp "$\tilde{x}_0$, Initial Control State (Reduced)"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
description ap "initial state of a control system; after model order reduction"@en

Initial Enzyme - Product 1 - Complex Concentration (Bi Bi Reaction Ordered - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialEnzymeProduct1ComplexConcentrationBiBiOrderedODEModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
defining formulation dp "$c_{EP_1}(t=0) = c_{{EP_1}_{0}}$"^^La Te X ep
in defining formulation dp "$c_{EP_1}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Enzyme - Product 1 - Product 2 - Complex Concentration (Bi Bi Reaction Ordered - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialEnzymeProduct1Product2ComplexConcentrationBiBiOrderedODEModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
defining formulation dp "$c_{EP_{1}P_{2}}(t=0) = c_{{EP_{1}P_{2}}_{0}}$"^^La Te X ep
in defining formulation dp "$c_{PS_{1}P_{2}}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Enzyme - Product 2 - Complex Concentration (Bi Bi Reaction Theorell-Chance - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialEnzymeProduct2ComplexConcentrationBiBiTheorellChanceODEModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Enzyme - Product 1 - Complex Concentration (Bi Bi Reaction Ordered - ODE Model) ni
defining formulation dp "$c_{EP_2}(t=0) = c_{{EP_2}_{0}}$"^^La Te X ep
in defining formulation dp "$c_{EP_2}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Enzyme - Substrate - Complex Concentration (Uni Uni Reaction - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialEnzymeSubstrateComplexConcentrationUniUniODEModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Enzyme-Substrate Complex Concentration ni
contains quantity op Time ni
defining formulation dp "$c_{ES}(t=0) = c_{{ES}_{0}}$"^^La Te X ep
in defining formulation dp "$c_{ES}$, Enzyme-Substrate Complex Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Enzyme - Substrate 1 - Complex Concentration (Bi Bi Reaction Ordered - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialEnzymeSubstrate1ComplexConcentrationBiBiOrderedODEModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Enzyme - Substrate 1 - Complex Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
defining formulation dp "$c_{ES_1}(t=0) = c_{{ES_1}_{0}}$"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Enzyme - Substrate 1 - Complex Concentration (Bi Bi Reaction Ping Pong - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialEnzymeSubstrate1ComplexConcentrationBiBiPingPongODEModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
defining formulation dp "$c_{ES_1}(t=0) = c_{{ES_1}_{0}}$"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Enzyme - Substrate 1 - Complex Concentration (Bi Bi Reaction Theorell-Chance - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialEnzymeSubstrate1ComplexConcentrationBiBiTheorellChanceODEModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Enzyme - Substrate 1 - Complex Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
defining formulation dp "$c_{ES_1}(t=0) = c_{{ES_1}_{0}}$"^^La Te X ep
defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep

Initial Enzyme - Substrate 1 - Substrate 2 - Complex Concentration (Bi Bi Reaction Ordered - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialEnzymeSubstrate1Substrate2ComplexConcentrationBiBiOrderedODEModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
defining formulation dp "$c_{ES_{1}S_{2}}(t=0) = c_{{ES_{1}S_{2}}_{0}}$"^^La Te X ep
in defining formulation dp "$c_{ES_{1}S_{2}}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Enzyme - Substrate 1 - Substrate 2 = Enzyme Product 1 - Product 2 - Complex Concentration (Bi Bi Reaction Ordered with single central Compelx - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialEnzymeSubstrate1Substrate2EnzymeProduct1Product2ComplexConcentrationBiBiOrderedODEModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
defining formulation dp "$c_{ES_{1}S_{2}=EP_{1}P_{2}}(t=0) = c_{{ES_{1}S_{2}=EP_{1}P_{2}}_{0}}$"^^La Te X ep
in defining formulation dp "$c_{ES_{1}S_{2}=EP_{1}P_{2}}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Enzyme Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialEnzymeConcentrationBiBiOrderedMichaelisMentenModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Enzyme Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model) ni
similar to formulation op Initial Enzyme Concentration (Uni Uni Reaction - Michaelis Menten Model) ni
defining formulation dp "$c_E(t=0) = c_{E_{0}}$"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Enzyme Concentration (Bi Bi Reaction Ordered - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialEnzymeConcentrationBiBiOrderedODEModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Enzyme Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
similar to formulation op Initial Enzyme Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni
similar to formulation op Initial Enzyme Concentration (Uni Uni Reaction - ODE Model) ni
defining formulation dp "$c_E(t=0) = c_{E_{0}}$"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Enzyme Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialEnzymeConcentrationBiBiPingPongMichaelisMentenModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
defining formulation dp "$c_E(t=0) = c_{E_{0}}$"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Enzyme Concentration (Bi Bi Reaction Ping Pong - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialEnzymeConcentrationBiBiPingPongODEModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
defining formulation dp "$c_E(t=0) = c_{E_{0}}$"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Enzyme Concentration (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialEnzymeConcentrationBiBiTheorellChanceMichaelisMentenModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Enzyme Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
similar to formulation op Initial Enzyme Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model) ni
similar to formulation op Initial Enzyme Concentration (Uni Uni Reaction - Michaelis Menten Model) ni
defining formulation dp "$c_E(t=0) = c_{E_{0}}$"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Enzyme Concentration (Bi Bi Reaction Theorell-Chance - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialEnzymeConcentrationBiBiTheorellChanceODEModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
defining formulation dp "$c_E(t=0) = c_{E_{0}}$"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Enzyme Concentration (Uni Uni Reaction - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialEnzymeConcentrationUniUniMichaelisMentenModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
defining formulation dp "$c_E(t=0) = c_{E_{0}}$"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Enzyme Concentration (Uni Uni Reaction - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialEnzymeConcentrationUniUniODEModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
defining formulation dp "$c_E(t=0) = c_{E_{0}}$"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Inhibitor Concentration (Uni Uni Reaction)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialInhibitorConcentrationUniUni

belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibitor Concentration ni
contains quantity op Time ni
defining formulation dp "$c_I(t=0) = c_{I_{0}}$"^^La Te X ep
in defining formulation dp "$c_I$, Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Intermediate - Substrate 2 - Complex Concentration (Bi Bi Reaction Ping Pong - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialIntermediateSubstrate2ComplexConcentrationBiBiPingPongODEModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
defining formulation dp "$c_{E*S_2}(t=0) = c_{E*S_2_{0}}$"^^La Te X ep
in defining formulation dp "$c_{E*S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Intermediate Concentration (Bi Bi Reaction Ping Pong - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialIntermediateConcentrationBiBiPingPongODEModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
defining formulation dp "$c_E*(t=0) = c_{E*_{0}}$"^^La Te X ep
defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$c_{E*}$, Concentration"^^La Te X ep

Initial Number Of Infected Citiesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialNumberOfInfectedCities

belongs to
Mathematical Formulation c
has facts
contains quantity op Number Of Infected Cities ni
contains quantity op Number of Regions ni
contains quantity op Time ni
defining formulation dp "$(i_m(t=0))_{m=1}^{N_R} = i(0)$"^^La Te X ep
in defining formulation dp "$N_R$, Number of Regions"^^La Te X ep
in defining formulation dp "$i_m(t)$, Number Of Infected Cities"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product 1 Concentration (Bi Bi Reaction Ordered - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProduct1ConcentrationBiBiOrderedODEModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Product 1 Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
defining formulation dp "$c_{P_1}(t=0) = c_{P_{1,0}}$"^^La Te X ep
in defining formulation dp "$c_P_1$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product 1 Concentration (Bi Bi Reaction Ordered with Product 1 - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProduct1ConcentrationBiBiOrderedwithProduct1MichaelisMentenModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Product 1 Concentration (Bi Bi Reaction Ordered - ODE Model) ni
defining formulation dp "$c_{P_1}(t=0) = c_{P_{1,0}}$"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product 1 Concentration (Bi Bi Reaction Ordered without Product 1 - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProduct1ConcentrationBiBiOrderedwithoutProduct1MichaelisMentenModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Product 2 Concentration (Bi Bi Reaction Ordered without Product 2 - Michaelis Menten Model) ni
defining formulation dp "$c_{P_1}(t=0) = 0$"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product 1 Concentration (Bi Bi Reaction Ping Pong - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProduct1ConcentrationBiBiPingPongODEModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Product 2 Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
similar to formulation op Initial Product Concentration (Uni Uni Reaction - ODE Model) ni
defining formulation dp "$c_{P_1}(t=0) = c_{P_{1,0}}$"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product 1 Concentration (Bi Bi Reaction Ping Pong with Product 1 - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProduct1ConcentrationBiBiwithProduct1MichaelisMentenModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Product 1 Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
defining formulation dp "$c_{P_1}(t=0) = c_{P_{1,0}}$"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product 1 Concentration (Bi Bi Reaction Ping Pong without Product 1 - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProduct1ConcentrationBiBiwithoutProduct1MichaelisMentenModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Product 2 Concentration (Bi Bi Reaction Ping Pong without Product 2 - Michaelis Menten Model) ni
defining formulation dp "$c_{P_1}(t=0) = 0$"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product 1 Concentration (Bi Bi Reaction Theorell-Chance - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProduct1ConcentrationBiBiTheorellChanceODEModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Product 1 Concentration (Bi Bi Reaction Ordered - ODE Model) ni
similar to formulation op Initial Product 2 Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni
defining formulation dp "$c_{P_1}(t=0) = c_{P_{1,0}}$"^^La Te X ep
in defining formulation dp "$c_P_1$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product 1 Concentration (Bi Bi Reaction Theorell-Chance with Product 1 - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProduct1ConcentrationBiBiTheorellChancewithProduct1MichaelisMentenModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Product 1 Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni
defining formulation dp "$c_{P_1}(t=0) = c_{P_{1,0}}$"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product 1 Concentration (Bi Bi Reaction Theorell-Chance without Product 1 - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProduct1ConcentrationBiBiTheorellChancewithoutProduct1MichaelisMentenModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Product 2 Concentration (Bi Bi Reaction Theorell-Chance without Product 2 - Michaelis Menten Model) ni
defining formulation dp "$c_{P_1}(t=0) = 0$"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product 2 Concentration (Bi Bi Reaction Ordered - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProduct2ConcentrationBiBiOrderedODEModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Product 2 Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
defining formulation dp "$c_{P_2}(t=0) = c_{P_{2,0}}$"^^La Te X ep
in defining formulation dp "$c_P_2$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product 2 Concentration (Bi Bi Reaction Ordered with Product 2 - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProduct2ConcentrationBiBiOrderedwithProduct2MichaelisMentenModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Product 2 Concentration (Bi Bi Reaction Ordered - ODE Model) ni
defining formulation dp "$c_{P_2}(t=0) = c_{P_{2,0}}$"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product 2 Concentration (Bi Bi Reaction Ordered without Product 2 - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProduct2ConcentrationBiBiOrderedwithoutProduct2MichaelisMentenModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Product 1 Concentration (Bi Bi Reaction Ordered without Product 1 - Michaelis Menten Model) ni
defining formulation dp "$c_{P_2}(t=0) = 0$"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product 2 Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProduct2ConcentrationBiBiMichaelisMentenModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Product 1 Concentration (Bi Bi Reaction Ping Pong with Product 1 - Michaelis Menten Model) ni
similar to formulation op Initial Product 2 Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
defining formulation dp "$c_{P_2}(t=0) = c_{P_{2,0}}$"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product 2 Concentration (Bi Bi Reaction Ping Pong - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProduct2ConcentrationBiBiPingPongODEModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
defining formulation dp "$c_{P_2}(t=0) = c_{P_{2,0}}$"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product 2 Concentration (Bi Bi Reaction Ping Pong with Product 2 - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProduct2ConcentrationBiBiwithProduct2MichaelisMentenModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
defining formulation dp "$c_{P_2}(t=0) = c_{P_{2,0}}$"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product 2 Concentration (Bi Bi Reaction Ping Pong without Product 2 - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProduct2ConcentrationBiBiwithoutProduct2MichaelisMentenModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
defining formulation dp "$c_{P_2}(t=0) = 0$"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product 2 Concentration (Bi Bi Reaction Theorell-Chance - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProduct2ConcentrationBiBiTheorellChanceODEModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
defining formulation dp "$c_{P_2}(t=0) = c_{P_{2,0}}$"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product 2 Concentration (Bi Bi Reaction Theorell-Chance with Product 2 - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProduct2ConcentrationBiBiTheorellChancewithProduct2MichaelisMentenModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Product 2 Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni
defining formulation dp "$c_{P_2}(t=0) = c_{P_{2,0}}$"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product 2 Concentration (Bi Bi Reaction Theorell-Chance without Product 2 - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProduct2ConcentrationBiBiTheorellChancewithoutProduct2MichaelisMentenModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Product 1 Concentration (Bi Bi Reaction Theorell-Chance without Product 1 - Michaelis Menten Model) ni
defining formulation dp "$c_{P_2}(t=0) = 0$"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product Concentration (Uni Uni Reaction - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProductConcentrationUniUniODEModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Product Concentration ni
contains quantity op Time ni
defining formulation dp "$c_{P}(t=0) = c_{P_{0}}$"^^La Te X ep
in defining formulation dp "$c_{P}$, Product Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product Concentration (Uni Uni Reaction with Product)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProductConcentrationUniUniwithProduct

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Product 2 Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
defining formulation dp "$c_{P}(t=0) = c_{P_0}$"^^La Te X ep
in defining formulation dp "$c_{P}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Product Concentration (Uni Uni Reaction without Product)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialProductConcentrationUniUniwithoutProduct

belongs to
Mathematical Formulation c
has facts
contains quantity op Product Concentration ni
contains quantity op Time ni
defining formulation dp "$c_{P}(t=0) = 0$"^^La Te X ep
in defining formulation dp "$c_{P}$, Product Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Quantum Densityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialQuantumDensity

initial density matrix of a quantum-mechanical system
belongs to
Mathematical Formulation c
has facts
contains quantity op Quantum Density Operator ni
contains quantity op Time ni
generalizes formulation op Initial Quantum State ni
defining formulation dp "$\rho(t=0)=\rho_0$"^^La Te X ep
in defining formulation dp "$\rho$, Quantum Density Operator"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Quantum Stateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialQuantumState

initial state vector of a quantum-mechanical system
belongs to
Mathematical Formulation c
has facts
contains quantity op Quantum State Vector ni
contains quantity op Time ni
defining formulation dp "$\psi(t=0)=\psi_0$"^^La Te X ep
in defining formulation dp "$\psi$, Quantum State Vector"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Reaction Rateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRate

belongs to
Quantity c
has facts
generalized by quantity op Reaction Rate ni
is dimensionless dp "false"^^boolean
description ap "instantaneous rate at the start of the reaction"@en

Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Product 1ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofBiBiReactionfollowingOrderedMechanismwithProduct1

Initial Rate of a Bi Bi Reaction following the Ordered Mechanism in the presence of Product 1
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni

Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Product 1 and single central Complexni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofBiBiReactionfollowingOrderedMechanismwithProduct1andSingleCC

Initial Rate of a Bi Bi Reaction following the Ordered Mechanism in the presence of Product 1 with a single central Complex
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni

Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Product 2ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofBiBiReactionfollowingOrderedMechanismwithProduct2

Initial Rate of a Bi Bi Reaction following the Ordered Mechanism in the presence of Product 2
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni

Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Product 2 and single central Complexni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofBiBiReactionfollowingOrderedMechanismwithProduct2andSingleCC

Initial Rate of a Bi Bi Reaction following the Ordered Mechanism in the presence of Product 2 with a single central Complex
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni

Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Products 1 and 2ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofBiBiReactionfollowingOrderedMechanismwithProducts1and2

Initial Rate of a Bi Bi Reaction following the Ordered Mechanism in the presence of Products 1 and 2
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni

Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism with Products 1 and 2 and single central Complexni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofBiBiReactionfollowingOrderedMechanismwithProducts1and2andSingleCC

Initial Rate of a Bi Bi Reaction following the Ordered Mechanism in the presence of Products 1 and 2 with a single central Complex
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni

Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism without Productsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofBiBiReactionfollowingOrderedMechanismwithoutProducts

Initial Rate of a Bi Bi Reaction following the Ordered Mechanism in the absence of products
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni

Initial Reaction Rate of Bi Bi Reaction following Ordered Mechanism without Products and single central Complexni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofBiBiReactionfollowingOrderedMechanismwithoutProductsandSingleCC

Initial Rate of a Bi Bi Reaction following the Ordered Mechanism in the absence of products with a single central Complex
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni

Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism with Product 1ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofBiBiReactionfollowingPingPongMechanismwithProduct1

Initial Rate of a Bi Bi Reaction following the Ping Pong Mechanism in the presence of Product 1
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni
generalizes problem op Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism without Products ni
similar to problem op Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism with Product 2 ni

Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism with Product 2ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofBiBiReactionfollowingPingPongMechanismwithProduct2

Initial Rate of a Bi Bi Reaction following the Ping Pong Mechanism in the presence of Product 2
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni
generalizes problem op Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism without Products ni
similar to problem op Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism with Product 1 ni

Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism with Products 1 and 2ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofBiBiReactionfollowingPingPongMechanismwithProducts1and2

Initial Rate of a Bi Bi Reaction following the Ping Pong Mechanism in the presence of Products 1 and 2
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni
generalizes problem op Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism with Product 1 ni
generalizes problem op Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism with Product 2 ni
generalizes problem op Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism without Products ni

Initial Reaction Rate of Bi Bi Reaction following Ping Pong Mechanism without Productsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofBiBiReactionfollowingPingPongMechanismwithoutProducts

Initial Rate of a Bi Bi Reaction following the Ping Pong Mechanism in the absence of Products
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni

Initial Reaction Rate of Bi Bi Reaction following Theorell-Chance Mechanism with Product 1ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofBiBiReactionfollowingTheorellChanceMechanismwithProduct1

Initial Rate of a Bi Bi Reaction following the Theorell-Chance Mechanism in the presence of Product 1
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni

Initial Reaction Rate of Bi Bi Reaction following Theorell-Chance Mechanism with Product 2ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofBiBiReactionfollowingTheorellChanceMechanismwithProduct2

Initial Rate of a Bi Bi Reaction following the Theorell-Chance Mechanism in the presence of Product 2
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni

Initial Reaction Rate of Bi Bi Reaction following Theorell-Chance Mechanism without Productsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofBiBiReactionfollowingTheorellChanceMechanismwithoutProducts

Initial Rate of a Bi Bi Reaction following the Theorell-Chance Mechanism in the absence of Products
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni

Initial Reaction Rate of Bi Bi Reaction following Theorell-Chance Mechanism withs Product 1 and 2ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofBiBiReactionfollowingTheorellChanceMechanismwithProducts1and2

Initial Rate of a Bi Bi Reaction following the Theorell-Chance Mechanism in the presence of Product 1 and 2
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni

Initial Reaction Rate of Uni Uni Reaction with Productni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateOfUniUniReactionWithProduct

Initial Rate of an Uni Uni Reaction in the presence of Product.
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni
generalized by problem op Uni Uni Reaction ni
generalizes problem op Initial Reaction Rate of Uni Uni Reaction without Product ni
modeled by op Uni Uni Reaction (Michaelis Menten Model with Product - Steady State Assumption) ni

Initial Reaction Rate of Uni Uni Reaction without Productni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateUniUniReactionWithoutProduct

Initial Rate of an Uni Uni Reaction in the absence of Product.
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni
modeled by op Uni Uni Reaction (Michaelis Menten Model without Product - Irreversibility Assumption) ni
modeled by op Uni Uni Reaction (Michaelis Menten Model without Product - Rapid Equilibrium Assumption) ni
modeled by op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni

Initial Reaction Rate of Uni Uni Reaction without Product and Competitive Complete Inhibitionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofUniUniReactionwithoutProductandCompetitiveCompleteInhibition

Initial Rate of an Uni Uni Reaction with competitive complete inhibition in the absence of Product.
belongs to
Research Problem c

Initial Reaction Rate of Uni Uni Reaction without Product and Competitive Partial Inhibitionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofUniUniReactionwithoutProductandCompetitivePartialInhibition

Initial Rate of an Uni Uni Reaction with competitive partial inhibition in the absence of Product.
belongs to
Research Problem c

Initial Reaction Rate of Uni Uni Reaction without Product and Mixed Complete Inhibitionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofUniUniReactionwithoutProductandMixedCompleteInhibition

Initial Rate of an Uni Uni Reaction with mixed complete inhibition in the absence of Product.
belongs to
Research Problem c

Initial Reaction Rate of Uni Uni Reaction without Product and Mixed Partial Inhibitionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofUniUniReactionwithoutProductandMixedPartialInhibition

Initial Rate of an Uni Uni Reaction with mixed partial inhibition in the absence of Product.
belongs to
Research Problem c

Initial Reaction Rate of Uni Uni Reaction without Product and Non-Competitive Complete Inhibitionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofUniUniReactionwithoutProductandNonCompetitiveCompleteInhibition

Initial Rate of an Uni Uni Reaction with non-competitive complete inhibition in the absence of Product.
belongs to
Research Problem c

Initial Reaction Rate of Uni Uni Reaction without Product and Non-Competitive Partial Inhibitionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofUniUniReactionwithoutProductandNonCompetitivePartialInhibition

Initial Rate of an Uni Uni Reaction with non-competitive partial inhibition in the absence of Product.
belongs to
Research Problem c

Initial Reaction Rate of Uni Uni Reaction without Product and Uncompetitive Complete Inhibitionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofUniUniReactionwithoutProductandUncompetitiveCompleteInhibition

Initial Rate of an Uni Uni Reaction with uncompetitive complete inhibition in the absence of Product.
belongs to
Research Problem c

Initial Reaction Rate of Uni Uni Reaction without Product and Uncompetitive Partial Inhibitionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialReactionRateofUniUniReactionwithoutProductandUncompetitivePartialInhibition

Initial Rate of an Uni Uni Reaction with uncompetitive partial inhibition in the absence of Product.
belongs to
Research Problem c

Initial Substrate 1 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialSubstrate1ConcentrationBiBiOrderedMichaelisMentenModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Substrate 1 Concentration (Bi Bi Reaction Ordered - ODE Model) ni
similar to formulation op Initial Substrate 2 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
defining formulation dp "$c_{S_1}(t=0) = c_{S_{1,0}}$"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Substrate 1 Concentration (Bi Bi Reaction Ordered - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialSubstrate1ConcentrationBiBiOrderedODEModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Substrate 1 Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
defining formulation dp "$c_{S_1}(t=0) = c_{S_{1,0}}$"^^La Te X ep
in defining formulation dp "$c_S_1$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Substrate 1 Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialSubstrate1ConcentrationBiBiMichaelisMentenModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Substrate 1 Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
similar to formulation op Initial Substrate 2 Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model) ni
defining formulation dp "$c_{S_1}(t=0) = c_{S_{1,0}}$"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Substrate 1 Concentration (Bi Bi Reaction Ping Pong - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialSubstrate1ConcentrationBiBiPingPongODEModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Substrate 2 Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
similar to formulation op Initial Substrate Concentration (Uni Uni Reaction - ODE Model) ni
defining formulation dp "$c_{S_1}(t=0) = c_{S_{1,0}}$"^^La Te X ep
in defining formulation dp "$c_S_1$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Substrate 1 Concentration (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialSubstrate1ConcentrationBiBiTheorellChanceMichaelisMentenModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Substrate 1 Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni
defining formulation dp "$c_{S_1}(t=0) = c_{S_{1,0}}$"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Substrate 1 Concentration (Bi Bi Reaction Theorell-Chance - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialSubstrate1ConcentrationBiBiTheorellChanceODEModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Substrate 1 Concentration (Bi Bi Reaction Ordered - ODE Model) ni
similar to formulation op Initial Substrate 2 Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni
defining formulation dp "$c_{S_1}(t=0) = c_{S_{1,0}}$"^^La Te X ep
in defining formulation dp "$c_S_1$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Substrate 2 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialSubstrate2ConcentrationBiBiOrderedMichaelisMentenModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Substrate 1 Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
similar to formulation op Initial Substrate 2 Concentration (Bi Bi Reaction Ordered - ODE Model) ni
defining formulation dp "$c_{S_2}(t=0) = c_{S_{2,0}}$"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Substrate 2 Concentration (Bi Bi Reaction Ordered - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialSubstrate2ConcentrationBiBiOrderedODEModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Substrate 2 Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
defining formulation dp "$c_{S_2}(t=0) = c_{S_{2,0}}$"^^La Te X ep
in defining formulation dp "$c_S_2$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Substrate 2 Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialSubstrate2ConcentrationBiBiMichaelisMentenModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Substrate 1 Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model) ni
similar to formulation op Initial Substrate 2 Concentration (Bi Bi Reaction Ping Pong - ODE Model) ni
defining formulation dp "$c_{S_2}(t=0) = c_{S_{2,0}}$"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Substrate 2 Concentration (Bi Bi Reaction Ping Pong - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialSubstrate2ConcentrationBiBiPingPongODEModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
defining formulation dp "$c_{S_2}(t=0) = c_{S_{2,0}}$"^^La Te X ep
in defining formulation dp "$c_S_2$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Substrate 2 Concentration (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialSubstrate2ConcentrationBiBiTheorellChanceMichaelisMentenModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Substrate 2 Concentration (Bi Bi Reaction Theorell-Chance - ODE Model) ni
defining formulation dp "$c_{S_2}(t=0) = c_{S_{2,0}}$"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Substrate 2 Concentration (Bi Bi Reaction Theorell-Chance - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialSubstrate2ConcentrationBiBiTheorellChanceODEModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Time ni
similar to formulation op Initial Substrate 2 Concentration (Bi Bi Reaction Ordered - ODE Model) ni
defining formulation dp "$c_{S_2}(t=0) = c_{S_{2,0}}$"^^La Te X ep
in defining formulation dp "$c_S_2$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Substrate Concentration (Uni Uni Reaction - ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialSubstrateConcentrationUniUniODEModel

belongs to
Mathematical Formulation c
has facts
contains quantity op Substrate Concentration ni
contains quantity op Time ni
defining formulation dp "$c_S(t=0) = c_{S_{0}}$"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Substrate Concentration (Uni Uni Reaction)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialSubstrateConcentrationUniUni

belongs to
Mathematical Formulation c
has facts
contains quantity op Substrate Concentration ni
contains quantity op Time ni
similar to formulation op Initial Substrate Concentration (Uni Uni Reaction - ODE Model) ni
defining formulation dp "$c_S(t=0) = c_{S_{0}}$"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep

Initial Value For Electron Scatteringni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InitialValueForElectronScattering

belongs to
Mathematical Formulation c
has facts
contained as initial condition in op Dynamical Electron Scattering Model ni
contains quantity op Amplitude Of Electron Wave ni
contains quantity op Reciprocal Lattice ni
contains quantity op Reciprocal Lattice Vectors ni
defining formulation dp "$\varphi_{\mathbf{g}}(0) =\delta_{\mathbf{0},\mathbf{g}} \quad \text{for } \mathbf{g}\in \Lambda_m^*$"^^La Te X ep
in defining formulation dp "$\Lambda^*_m$, Reciprocal Lattice"^^La Te X ep
in defining formulation dp "$\varphi_{\mathbf{g}}(0)$, Amplitude of Electron Wave"^^La Te X ep
in defining formulation dp "$g$, Reciprocal Lattice Vectors"^^La Te X ep
description ap "initial value for electron scattering, used for modeling of transmission electron microscopy"@en

Integer Number (Dimensionless)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#IntegerDimensionless

Number that can be written without a fractional or decimal component
belongs to
Quantity Kind c
has facts
is dimensionless dp "true"^^boolean
wikidata I D ap Q12503 ep

Integral Of The Population Density Fraction Of Exposed (Initial Condition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#IntegralOfThePopulationDensityFractionOfExposedInitialCondition

belongs to
Mathematical Formulation c
has facts
contained as initial condition in op PDE SEIR Model ni
contains quantity op Coefficient Scaling Infectious To Exposed ni
contains quantity op Fraction Of Population Density Of Exposed ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Total Population Density ni
defining formulation dp "$\int_{\Omega^{(l)}} e(x, 0) n(x) d x=\Sigma_{\mathcal{E}} \hat{\mathcal{I}}^{(l)}$"^^La Te X ep
in defining formulation dp "$\Sigma_{\mathcal{E}}$, Coefficient Scaling Infectious To Exposed"^^La Te X ep
in defining formulation dp "$\hat{\mathcal{I}}^{(l)}$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$e(x, 0)$, Fraction Of Population Density Of Exposed"^^La Te X ep
in defining formulation dp "$n(x)$, Total Population Density"^^La Te X ep

Integral Of The Population Density Fraction Of Infectious (Initial Condition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#IntegralOfThePopulationDensityFractionOfInfectiousInitialCondition

belongs to
Mathematical Formulation c
has facts
contained as initial condition in op PDE SEIR Model ni
contains quantity op Fraction Of Population Density Of Infectious ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Total Population Density ni
defining formulation dp "$\int_{\Omega^{(l)}} i(x, 0) n(x) d x=\hat{\mathcal{I}}^{(l)}$"^^La Te X ep
in defining formulation dp "$\hat{\mathcal{I}}^{(l)}$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$i(x, 0)$, Fraction Of Population Density Of Infectious"^^La Te X ep
in defining formulation dp "$n(x)$, Total Population Density"^^La Te X ep

Integral Of The Population Density Fraction Of Susceptibles (Initial Condition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#IntegralOfThePopulationDensityFractionOfSusceptiblesInitialCondition

belongs to
Mathematical Formulation c
has facts
contained as initial condition in op PDE SEIR Model ni
contains quantity op Coefficient Scaling Infectious To Exposed ni
contains quantity op Fraction Of Population Density Of Susceptibles ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Removed Individuals ni
contains quantity op Total Population Density ni
contains quantity op Total Population Size ni
defining formulation dp "$ \int_{\Omega^{(l)}} s(x, 0) n(x) dx = \hat{\mathcal{N}}_l-\left(1+\Sigma_{\mathcal{E}}\right) \hat{\mathcal{I}}^{(l)}-\hat{\mathcal{R}}^{(l)} $"^^La Te X ep
in defining formulation dp "$\Sigma_{\mathcal{E}}$, Coefficient Scaling Infectious To Exposed"^^La Te X ep
in defining formulation dp "$\hat{\mathcal{I}}^{(l)}$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$\hat{\mathcal{R}}^{(l)}$, Number Of Removed Individuals"^^La Te X ep
in defining formulation dp "$hat{\mathcal{N}}_l$, Total Population Size"^^La Te X ep
in defining formulation dp "$n(x)$, Total Population Density"^^La Te X ep
in defining formulation dp "$s(x, 0)$, Fraction Of Population Density Of Susceptibles"^^La Te X ep

Integral Of The Total Population Density (Initial Condition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#IntegralOfTheTotalPopulationDensityInitialCondition

Integral Of The Total Population Density Initial Condition
belongs to
Mathematical Formulation c
has facts
contained as initial condition in op PDE SEIR Model ni
contains quantity op Total Population Density ni
contains quantity op Total Population Size ni
defining formulation dp "$\int_{\Omega^{(l)}} n(x) d x=\hat{\mathcal{N}}_l$"^^La Te X ep
in defining formulation dp "$hat{\mathcal{N}}_l$, Total Population Size"^^La Te X ep
in defining formulation dp "$n(x)$, Total Population Density"^^La Te X ep

Interaction Forceni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InteractionForce

belongs to
Quantity c
has facts
is dimensionless dp "false"^^boolean
description ap "interaction force on individual by media and influencers"@en

Interaction Force On An Individualni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InteractionForceOnAnIndividual

The interaction force on individual i is given by a weighted sum of attractive forces from all other connected individuals j, the respective media and the respective influencer scaled by the parameters a,b,c > 0 respectively.
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Opinion Model With Influencers And Media ni
contains quantity op Influencer Individual Matrix ni
contains quantity op Interaction Force ni
contains quantity op Interaction Weight ni
contains quantity op Medium Follower Matrix ni
contains quantity op Parameter To Scale Attractive Force From Influencers ni
contains quantity op Parameter To Scale Attractive Force From Media ni
contains quantity op Parameter To Scale Attractive Force From Other Individuals ni
contains quantity op Time ni
defining formulation dp "$F_i(\mathbf{x}, \mathbf{y}, \mathbf{z}, t)=\frac{a}{\sum_{j^{\prime}} w_{i j^{\prime}}(t)} \sum_{j=1}^N w_{i j}(t)\left(x_j(t)-x_i(t)\right)+b \sum_{m=1}^M B_{i m}(t)\left(y_m(t)-x_i(t)\right)+c \sum_{l=1}^L C_{i l}(t)\left(z_l(t)-x_i(t)\right)$"
in defining formulation dp "$B(t)$, Medium Follower Matrix"^^La Te X ep
in defining formulation dp "$C(t)$, Influencer Individual Matrix"^^La Te X ep
in defining formulation dp "$F_i(t)$, Interaction Force"^^La Te X ep
in defining formulation dp "$a$, Parameter To Scale Attractive Force From Other Individuals"^^La Te X ep
in defining formulation dp "$b$, Parameter To Scale Attractive Force From Media"^^La Te X ep
in defining formulation dp "$c$, Parameter To Scale Attractive Force From Influencers"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$w_{ij}$, Interaction Weight"^^La Te X ep
is space-continuous dp "true"^^boolean
is time-continuous dp "true"^^boolean

Interaction Weightni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InteractionWeight

Interaction Weight
belongs to
Quantity c

Interaction Weight Between Individualsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InteractionWeightBetweenIndividuals

The interaction weights between pairs of individuals i and j
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Opinion Model With Influencers And Media ni
contains quantity op Individual Relationship Matrix ni
contains quantity op Interaction Weight ni
contains quantity op Opinion Vector of Individuals ni
contains quantity op Pair Function ni
contains quantity op Time ni
defines op Interaction Weight ni
defining formulation dp "$ w_{ij}(t) = A_{ij}(t) \phi (|| x_j(t) - x_i(t)|| )$"^^La Te X ep
in defining formulation dp "$A(t)$, Individual Relationship Matrix"^^La Te X ep
in defining formulation dp "$\phi$, Pair Function"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$w_{ij}(t)$, Interaction Weight"^^La Te X ep
in defining formulation dp "$x(t)$, Opinion Vector of Individuals"^^La Te X ep
is space-continuous dp "true"^^boolean

Intermediate - Substrate 2 - Complex Concentration ODE (Bi Bi Reaction Ping Pong)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#IntermediateSubstrate2ComplexConcentrationODEBiBiPingPong

Ordinary differential equation describing the intermediate-substrate complex concentration over time in a bi bi enzymatic reaction following the ping pong mechanism.
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{E*S_2}}{dt} = k_{3} * c_{E*} * c_{S_2} + k_{-4} * c_{E} * c_{P_2} - k_{-3} * c_{E*S_2} - k_{4} * c_{E*S_2}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{E*S_2}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{E*S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E*}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep

Intermediate - Substrate 2 Complex Concentrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#IntermediateSubstrate2ComplexConcentration

belongs to
Quantity c
has facts
generalized by quantity op Concentration ni
description ap "amount of intermediate - substrate 2 complex present in a reaction environment"@en

Intermediate Concentrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#IntermediateConcentration

belongs to
Quantity c
has facts
generalized by quantity op Concentration ni
description ap "amount of intermediate present in a reaction environment"@en

Intermediate Concentration ODE (Bi Bi Reaction Ping Pong)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#IntermediateConcentrationODEBiBiPingPong

Ordinary differential equation describing the intermediate concentration over time in a bi bi enzymatic reaction following the ping pong mechanism.
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{E*}}{dt} = k_{2} * c_{ES_1} + k_{-3} * c_{E*S_2} - k_{-2} * c_{E*} * c_{P_1} - k_{3} * c_{E*} * c_{S_2}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{E*}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{E*S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E*}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep

Intermolecular Potentialni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#IntermolecularPotential

Intermolecular potential energy function that describes the interactions between molecules. Typically, Intermolecular forces are weak relative to intramolecular forces.
belongs to
Quantity c
has facts
description ap "energy function that describes the interactions between molecules"@en
wikidata I D ap Q245031 ep

International Classification of Diseases - 9ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InternationalClassificationOfDiseases9

belongs to
Quantity c
has facts
description ap "identifier of drugs in the ICD catalogue"@en
wikidata I D ap Q14067712 ep

Ion Currentni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#IonCurrent

belongs to
Quantity c
has facts
generalized by quantity op Electric Current ni
description ap "flow of electrical charge observed in electrolytes, wires, plasma, and other conducting materials or fluids"@en
qudt I D ap Ion Current ep
wikidata I D ap Q6063423 ep

Irreversibility Assumptionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#IrreversibilityAssumption

belongs to
Mathematical Formulation c
has facts
contains quantity op Complexed Enzyme Concentration ni
contains quantity op Product Concentration ni
defining formulation dp "$\frac{c_{EX}}{c_P} \ggt 1$"^^La Te X ep
in defining formulation dp "$c_P$, Product Concentration"^^La Te X ep
in defining formulation dp "$c_{EX}$, Complexed Enzyme Concentration"^^La Te X ep

Isotropic Gaussian Functionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#IsotropicGaussianFunction

Isotropic Gaussian Function located at the center of the respective province used in the PDE SEIR Model for representing density and density fractions
belongs to
Quantity c
has facts
description ap "Gaussian function representing density and density fractions of provinces"@en

Isotropic Gaussian Function Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#IsotropicGaussianFunctionFormulation

Isotropic Gaussian Function located at the center of the respective province used in the PDE SEIR Model for representing density and density fractions
belongs to
Mathematical Formulation c
has facts
contained as formulation in op PDE SEIR Model ni
contains quantity op Center Of Province ni
contains quantity op Isotropic Gaussian Function ni
contains quantity op Pi Number ni
contains quantity op Variance ni
defining formulation dp "$G^{(l)}(x) \equiv \frac{1}{2\pi\sigma^2}\text{exp}(-\frac{||x-x_0^{(l)}||^2}{2\sigma^2})$"^^La Te X ep
in defining formulation dp "$G^{(l)}(x)$, Isotropic Gaussian Function"^^La Te X ep
in defining formulation dp "$\pi$, Pi Number"^^La Te X ep
in defining formulation dp "$\sigma$, Variance"^^La Te X ep
in defining formulation dp "$x_0^{(l)}$, Center Of Province"^^La Te X ep

Jahnke (2022) Efficient Numerical Simulation of Soil-Tool Interactionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Jahnke_2022_Efficient_Numerical_Simulation_of_Soil-Tool_Interaction

belongs to
Publication c
has facts
doi I D ap publica 340 ep

Koprucki (2017) Numerical methods for drift-diffusion modelsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Koprucki_2017_Numerical_methods_for_drift-diffusion_models

Handbook of Optoelectronic Device Modeling and Simulation, Chapter = 50, Editor = Joachim Piprek, Pages = 733-771, Title = Drift-Diffusion Models, publisher = CRC Press, Volume = 2, Year = 2017
belongs to
Publication c
has facts
doi I D ap W I A S. P R E P R I N T.2263 ep

Kostré (2022) Understanding the romanization spreading on historical interregional networks in Northern Tunisiani back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Kostre_2022_Understanding_the_romanization_spreading_on_historical_interregional_networks_in_Northern_Tunisia

belongs to
Publication c
has facts
invents op Susceptible Infectious Epidemic Spreading Model ni
studies op Romanization Spreading in Northern Tunesia ni
doi I D ap s41109 022 00492 w ep
wikidata I D ap Q115136310 ep

Lagrange Multiplierni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LagrangeMultiplier

belongs to
Quantity c
has facts
generalizes quantity op Control System Lagrange Multiplier ni
description ap "method to solve constrained optimization problems"@en
wikidata I D ap Q598870 ep

Laplace Equation For The Electric Potentialni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LaplaceEquationForTheElectricPotential

belongs to
Mathematical Formulation c
has facts
contains quantity op Electric Potential ni
contains quantity op Permittivity (Dielectric) ni
generalized by formulation op Poisson Equation For The Electric Potential ni
defining formulation dp "$-\nabla\left(\epsilon_s\nabla\phi\right)=0$"^^La Te X ep
in defining formulation dp "$\epsilon_s$, Permittivity (Dielectric)"^^La Te X ep
in defining formulation dp "$\phi$, Electric Potential"^^La Te X ep
description ap "in electrostatics, the Laplace equation characterizes the electrostatic potential in the absence of charges"@en
wikidata I D ap Q339444 ep

Lengthni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Length

Measured dimension of an object
belongs to
Quantity Kind c
has facts
qudt I D ap Length ep
wikidata I D ap Q36253 ep

Length Of Unit Cellni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LengthOfUnitCell

belongs to
Quantity c
has facts
generalized by quantity op Length ni
description ap "defines the size of the repeating unit in a crystal structure"@en

Leskovac (2003) Comprehensive Enzyme Kineticsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Leskovac_2003_Comprehensive_Enzyme_Kinetics

Vrvic, Miroslav. (2003). Comprehensive enzyme kinetics by V. Leskovac, Published by Kluwer Academic/Plenum Plblisher New York, March 2003-11-17. Journal of The Serbian Chemical Society - J SERB CHEM SOC. 68. 1011-1013
belongs to
Publication c
has facts
surveys op Enzyme Kinetics ni
doi I D ap J S C0312011 V ep

Level Of Mortalityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LevelOfMortality

belongs to
Quantity c
has facts
description ap "rate at which individuals in a population die over a specified period"@en

Likelihood Valueni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LikelihoodValue

measure used in statistics to quantify how well a given set of model parameters explains observed data
belongs to
Quantity c
has facts
description ap "probability density of observed data viewed as a function of the parameters of a statistical model"@en
wikidata I D ap Q45284 ep

Limiting Distribution Of Individualsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LimitingDistributionOfIndividuals

belongs to
Quantity c
has facts
description ap "limiting distribution of individuals"@en

Limiting Distribution Of Individuals Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LimitingDistributionOfIndividualsFormulation

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Partial Mean Field Opinion Model ni
contains assumption op Number Of Individuals Tends To Infinity Assumption ni
contains quantity op Attraction Force At Opinion ni
contains quantity op Limiting Distribution Of Individuals ni
contains quantity op Noise Strength ni
contains quantity op Opinion ni
contains quantity op Rate Of Switching Influencers ni
contains quantity op Time ni
generalized by op Empirical Distribution Of Individuals Formulation ni
defining formulation dp "$\partial_t \rho_{m, l}(x, t)=\frac{1}{2} \sigma^2 \Delta \rho_{m, l}(x, t)-\nabla \cdot\left(\rho_{m, l}(x, t) \mathcal{F} \left(x, y_m, z_l, \rho\right)\right) \quad+\sum_{l^{\prime} \neq l}\left(-\Lambda_m^{\rightarrow l^{\prime}}(x, t) \rho_{m, l}(x, t)+\Lambda_m^{\rightarrow l}(x, t) \rho_{m, l^{\prime}}(x, t)\right)$"^^La Te X ep
in defining formulation dp "$\Lambda_m^{\rightarrow l}$, Rate Of Switching Influencers"^^La Te X ep
in defining formulation dp "$\mathcal{F}$, Attraction Force at Opinion"^^La Te X ep
in defining formulation dp "$\partial_t \rho_{m, l}(x, t)$, Limiting Distribution Of Individuals"^^La Te X ep
in defining formulation dp "$\sigma$, Noise Strength"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$x$, Opinion"^^La Te X ep
in defining formulation dp "$y_m$, Opinion"^^La Te X ep
in defining formulation dp "$z_l$, Opinion"^^La Te X ep

Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Backward)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LimitingReactionRateBackwardBiBiReactionOrdered

Maximal initial reaction rate of Bi Bi Reaction with Ordered Mechanism in the backward direction.
belongs to
Quantity c
has facts
defined by op Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Backward, Definition) ni
generalized by quantity op Reaction Rate ni
description ap "limiting reaction rate"@en

Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Backward, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LimitingReactionRateBackwardBiBiReactionOrderedDefinition

Definition of the Limiting Reaction Rate in a Bi Bi Reaction with Ordered Mechanism in the backward direction.
belongs to
Mathematical Formulation c
has facts
contains quantity op Enzyme Concentration ni
contains quantity op Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Backward) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$V_{max,b} \equiv \frac{k_{-1} * k_{-2} * k_{-3}}{k_{-1} * k_{-2} + k_{-1} * k_3 + k_{-1} * k_{-3} + k_{-2} * k_{-3}} * c_{E_0}$"^^La Te X ep
in defining formulation dp "$V_{max,b}$, Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Backward)"^^La Te X ep
in defining formulation dp "$c_{E_{0}}$, Enzyme Concentration"^^La Te X ep
in defining formulation dp "$k_3$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean

Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Forward)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LimitingReactionRateForwardBiBiReactionOrdered

Maximal initial reaction rate of Bi Bi Reaction with Ordered Mechanism in the forward direction.
belongs to
Quantity c
has facts
defined by op Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Forward, Definition) ni
generalized by quantity op Reaction Rate ni
description ap "limiting reaction rate"@en

Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Forward, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LimitingReactionRateForwardBiBiReactionOrderedDefinition

Definition of the Limiting Reaction Rate in a Bi Bi Reaction with Ordered Mechanism in the forward direction.
belongs to
Mathematical Formulation c
has facts
contains quantity op Enzyme Concentration ni
contains quantity op Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Forward) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$V_{max,f} \equiv \frac{k_3 * k_4 * k_5}{k_4 +k_5 + k_3 * k_4 + k_3 * k_5 + k_{-3} * k_5} * c_{E_0}$"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Forward)"^^La Te X ep
in defining formulation dp "$c_{E_{0}}$, Enzyme Concentration"^^La Te X ep
in defining formulation dp "$k_3$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_4$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_5$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean

Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism with single central Complex - Forward)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LimitingReactionRateForwardBiBiReactionOrderedsingleCC

Maximal initial reaction rate of Bi Bi Reaction with Ordered Mechanism and single central Complex in the forward direction.
belongs to
Quantity c
has facts
defined by op Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism with single central Complex - Forward, Definition) ni
generalized by quantity op Reaction Rate ni
description ap "limiting reaction rate"@en

Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism with single central Complex - Forward, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LimitingReactionRateForwardBiBiReactionOrderedsingleCCDefinition

Definition of the Limiting Reaction Rate in a Bi Bi Reaction with Ordered Mechanism and single central Complex in the forward direction.
belongs to
Mathematical Formulation c
has facts
contains quantity op Enzyme Concentration ni
contains quantity op Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism with single central Complex - Forward) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$V_{max,f} \equiv \frac{k_4 * k_5}{k_4 +k_5} * c_{E_0}$"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism with single central Complex - Forward)"^^La Te X ep
in defining formulation dp "$c_{E_{0}}$, Enzyme Concentration"^^La Te X ep
in defining formulation dp "$k_4$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_5$, Reaction Rate Constant"^^La Te X ep

Limiting Reaction Rate (Uni Uni Reaction - Backward)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LimitingReactionRateUniUniReactionBackward

Maximal initial reaction rate of Uni Uni Reaction in the backward direction.
belongs to
Quantity c
has facts
defined by op Limiting Reaction Rate (Uni Uni Reaction - Backward, Definition) ni
generalized by quantity op Reaction Rate ni
is dimensionless dp "false"^^boolean
description ap "limiting reaction rate"@en

Limiting Reaction Rate (Uni Uni Reaction - Backward, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LimitingReactionRateUniUniReactionBackwardDefinition

Definition of the Limiting Reaction Rate in an Uni Uni Reaction in the backward direction.
belongs to
Mathematical Formulation c
has facts
contains quantity op Enzyme Concentration ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Backward) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$V_{max,b} \equiv k_{-2} * c_{E_0}$"^^La Te X ep
in defining formulation dp "$V_{max,b}$, Limiting Reaction Rate (Uni Uni Reaction - Backward)"^^La Te X ep
in defining formulation dp "$c_{E_{0}}$, Enzyme Concentration"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean

Limiting Reaction Rate (Uni Uni Reaction - Forward)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LimitingReactionRateUniUniReactionForward

Maximal initial reaction rate of Uni Uni Reaction in the forward direction.
belongs to
Quantity c
has facts
defined by op Limiting Reaction Rate (Uni Uni Reaction - Forward, Definition) ni
generalized by quantity op Reaction Rate ni
is dimensionless dp "false"^^boolean
description ap "limiting reaction rate"@en

Limiting Reaction Rate (Uni Uni Reaction - Forward, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LimitingReactionRateUniUniReactionForwardDefinition

Definition of the Limiting Reaction Rate in an Uni Uni Reaction in the forward direction.
belongs to
Mathematical Formulation c
has facts
contains quantity op Enzyme Concentration ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$V_{max,f} \equiv k_2 * c_{E_0}$"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_{E_{0}}$, Enzyme Concentration"^^La Te X ep
in defining formulation dp "$k_2$, Reaction Rate Constant"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean

Limiting Reaction Rate Backward (Bi Bi Reaction Ordered - Single central Complex)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LimitingReactionRateBackwardBiBiReactionOrderedsingleCC

belongs to
Mathematical Formulation c
has facts
contains initial condition op Initial Enzyme Concentration (Bi Bi Reaction Ordered - Michaelis Menten Model) ni
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
defining formulation dp "$V_2 = \frac{k_{-1} * k_{-2}}{k_{-1} +k_{-2}} * c_{E_0}$"^^La Te X ep
in defining formulation dp "$V_2$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{E_{0}}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep

Limiting Reaction Rate Backward (Bi Bi Reaction Ping Pong)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LimitingReactionRateBackwardBiBiReactionPingPong

belongs to
Mathematical Formulation c
has facts
contains initial condition op Initial Enzyme Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model) ni
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
defining formulation dp "$V_{2} = \frac{k_{-1} * k_{-3}}{k_{-1} + k_{-3}} * c_{E_{0}}$"^^La Te X ep
in defining formulation dp "$V_2$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{E_{0}}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep

Limiting Reaction Rate Backward (Bi Bi Reaction Theorell-Chance)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LimitingReactionRateBackwardBiBiReactionTheorellChance

belongs to
Mathematical Formulation c
has facts
contains initial condition op Initial Enzyme Concentration (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model) ni
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
defining formulation dp "$V_2 = k_{-1} * c_{E_0}$"^^La Te X ep
in defining formulation dp "$V_2$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{E_{0}}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep

Limiting Reaction Rate Forward (Bi Bi Reaction Ping Pong)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LimitingReactionRateForwardBiBiReactionPingPong

belongs to
Mathematical Formulation c
has facts
contains initial condition op Initial Enzyme Concentration (Bi Bi Reaction Ping Pong - Michaelis Menten Model) ni
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
defining formulation dp "$V_{1} = \frac{k_{2} * k_{4}}{k_{2} + k_{4}} * c_{E_{0}}$"^^La Te X ep
in defining formulation dp "$V_1$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{E_{0}}$, Concentration"^^La Te X ep
in defining formulation dp "$k_2$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_4$, Reaction Rate Constant"^^La Te X ep

Limiting Reaction Rate Forward (Bi Bi Reaction Theorell-Chance)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LimitingReactionRateForwardBiBiReactionTheorellChance

belongs to
Mathematical Formulation c
has facts
contains initial condition op Initial Enzyme Concentration (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model) ni
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
defining formulation dp "$V_1 = k_3 * c_{E_0}$"^^La Te X ep
in defining formulation dp "$V_1$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{E_{0}}$, Concentration"^^La Te X ep
in defining formulation dp "$k_3$, Reaction Rate Constant"^^La Te X ep

Limiting Reaction Rate with Inhibitor (Uni Uni Reaction - Forward)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LimitingReactionRateUniUniReactionForwardWithInhibitor

Forward Limiting Reaction Rate with Inhibitor in an Uni Uni Reaction
belongs to
Quantity c
has facts
defined by op Limiting Reaction Rate with Inhibitor (Uni Uni Reaction - Forward, Definition) ni
generalized by quantity op Reaction Rate ni
is dimensionless dp "false"^^boolean
description ap "limiting reaction rate"@en

Limiting Reaction Rate with Inhibitor (Uni Uni Reaction - Forward, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LimitingReactionRateUniUniReactionForwardWithInhibitorDefinition

Definition of the Limiting Reaction Rate in an Uni Uni Reaction with Inhibitor in the forward direction.
belongs to
Mathematical Formulation c
has facts
contains quantity op Enzyme Concentration ni
contains quantity op Limiting Reaction Rate with Inhibitor (Uni Uni Reaction - Forward) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$V_{max,I,f} \equiv k_{6} * c_{E_0}$"^^La Te X ep
in defining formulation dp "$V_{max,I,f}$, Limiting Reaction Rate with Inhibitor (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_{E_0}$, Enzyme Concentration"^^La Te X ep
in defining formulation dp "$k_{6}$, Reaction Rate Constant"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean

Line Conceptni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LineConcept

A line concept $(mathcal{L}, f )$ is a set of lines $mathcal{L}$ together with their frequencies $f_l$ for all $l \in L$. The frequency $f_l$ of a line $l$ says how often service is offered along line $l$ within a given time period $I$ (e.g., an hour, a day).
belongs to
Mathematical Formulation c
has facts
contains quantity op Frequency ni
contains quantity op PTN Line ni
defining formulation dp "$(\mathcal{L},f)$"^^La Te X ep
in defining formulation dp "$\mathcal{L}$, PTNLine"^^La Te X ep
in defining formulation dp "$f_l$, Frequncy$"^^La Te X ep

Line Concept Costsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LineConceptCosts

The costs for a line concept
belongs to
Mathematical Formulation c
has facts
contains formulation op Line Concept ni
contains formulation op Line Costs Computation ni
contains quantity op Costs ni
contains quantity op Costs of Line Concept ni
contains quantity op Frequency ni
defining formulation dp "$cost(\mathcal{L},f)=\sum_{l \in \mathcal{L}} f_l \cdot cost_l$"^^La Te X ep
in defining formulation dp "$\mathcal{L},f)$, Line Concept"^^La Te X ep
in defining formulation dp "$cost(\mathcal{L},f)$,Costs of Line Concept"^^La Te X ep
in defining formulation dp "$cost_l$, Costs"^^La Te X ep
in defining formulation dp "$f_l$, Frequency"^^La Te X ep

Line Costs Computationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LineCostsComputation

Sum of all costs of a single line
belongs to
Mathematical Formulation c
has facts
contains quantity op Costs ni
contains quantity op Costs per Unit ni
contains quantity op Duration ni
contains quantity op Fixed Costs ni
contains quantity op Graph Type Identifier ni
contains quantity op Length ni
contains quantity op Period Length ni
contains quantity op Turn Over Time ni
defining formulation dp "$cost_l=costs\_fixed+\sum_{e \in l}\left(costs\_length \cdot length_e + costs\_edges\right) + costs\_vehicles \cdot \lvert x \cdot \frac{duration_l + turn\_over\_time}{period\_length}\rvert$"^^La Te X ep
in defining formulation dp "$cost_l$, Costs"^^La Te X ep
in defining formulation dp "$costs\_edges$, Costs"^^La Te X ep
in defining formulation dp "$costs\_fixed$, Fixed Costs"^^La Te X ep
in defining formulation dp "$costs\_length$, Costs per Unit"^^La Te X ep
in defining formulation dp "$costs\_vehicles$, Costs"^^La Te X ep
in defining formulation dp "$duration_l$, Duration"^^La Te X ep
in defining formulation dp "$length_e$, Length"^^La Te X ep
in defining formulation dp "$period\_length$, Period Length"^^La Te X ep
in defining formulation dp "$turn\_over\_time$, Turn Over Time"^^La Te X ep
in defining formulation dp "$x$,Graph Type Identifier"^^La Te X ep

Linear Discrete Element Methodni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Linear_Discrete_Element_Method

belongs to
Mathematical Model c
has facts
contained in model op Recurrent Neural Network Surrogate for Discrete Element Method ni
generalized by model op Discrete Element Method ni
description ap "computational technique used to simulate the behaviour of granular materials, powders and other particulate systems"@en

Linear Parameter Estimation (Uni Uni Reaction without Product - Eadie Hofstee Model - Irreversibility Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearParameterEstimationUniUniReactionWithoutProductEHIrreversibility

linear fit to determine the limiting reaction rate and michaelis constant
belongs to
Computational Task c
has facts
contains formulation op Eadie Hofstee Equation (Uni Uni Reaction without Product - Irreversibility Assumption) ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Irreversibility Assumption) ni
generalized by task op Linear Parameter Estimation of Enzyme Kinetics ni
linearizes task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product - Michaelis Menten Model - Irreversibility Assumption) ni
is linear dp "true"^^boolean

Linear Parameter Estimation (Uni Uni Reaction without Product - Eadie Hofstee Model - Rapid Equilibrium Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearParameterEstimationUniUniReactionWithoutProductEHRapidEquilibrium

linear fit to determine the limiting reaction rate and michaelis constant
belongs to
Computational Task c
has facts
contains formulation op Eadie Hofstee Equation (Uni Uni Reaction without Product - Rapid Equilibrium Assumption) ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Rapid Equilibrium Assumption) ni
generalized by task op Linear Parameter Estimation of Enzyme Kinetics ni
linearizes task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product - Michaelis Menten Model - Rapid Equilibrium Assumption) ni
is linear dp "true"^^boolean

Linear Parameter Estimation (Uni Uni Reaction without Product - Eadie Hofstee Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearParameterEstimationUniUniReactionWithoutProductEHSteadyState

linear fit to determine the limiting reaction rate and michaelis constant
belongs to
Computational Task c
has facts
contains formulation op Eadie Hofstee Equation (Uni Uni Reaction without Product - Steady State Assumption) ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
generalized by task op Linear Parameter Estimation of Enzyme Kinetics ni
linearizes task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product - Michaelis Menten Model - Steady State Assumption) ni
is linear dp "true"^^boolean

Linear Parameter Estimation (Uni Uni Reaction without Product - Hanes Woolf Model - Irreversibility Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearParameterEstimationUniUniReactionWithoutProductHWIrreversibility

linear fit to determine the limiting reaction rate and michaelis constant
belongs to
Computational Task c
has facts
contains formulation op Hanes Woolf Equation (Uni Uni Reaction without Product - Irreversibility Assumption) ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Irreversibility Assumption) ni
generalized by task op Linear Parameter Estimation of Enzyme Kinetics ni
linearizes task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product - Michaelis Menten Model - Irreversibility Assumption) ni
is linear dp "true"^^boolean

Linear Parameter Estimation (Uni Uni Reaction without Product - Hanes Woolf Model - Rapid Equilibrium Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearParameterEstimationUniUniReactionWithoutProductHWRapidEquilibrium

linear fit to determine the limiting reaction rate and michaelis constant
belongs to
Computational Task c
has facts
contains formulation op Hanes Woolf Equation (Uni Uni Reaction without Product - Rapid Equilibrium Assumption) ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Rapid Equilibrium Assumption) ni
generalized by task op Linear Parameter Estimation of Enzyme Kinetics ni
linearizes task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product - Michaelis Menten Model - Rapid Equilibrium Assumption) ni
is linear dp "true"^^boolean

Linear Parameter Estimation (Uni Uni Reaction without Product - Hanes Woolf Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearParameterEstimationUniUniReactionWithoutProductHWSteadyState

linear fit to determine the limiting reaction rate and michaelis constant
belongs to
Computational Task c
has facts
contains formulation op Hanes Woolf Equation (Uni Uni Reaction without Product - Steady State Assumption) ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
generalized by task op Linear Parameter Estimation of Enzyme Kinetics ni
linearizes task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product - Michaelis Menten Model - Steady State Assumption) ni
is linear dp "true"^^boolean

Linear Parameter Estimation (Uni Uni Reaction without Product - Lineweaver Burk Model - Irreversibility Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearParameterEstimationUniUniReactionWithoutProductLBIrreversibility

linear fit to determine the limiting reaction rate and michaelis constant
belongs to
Computational Task c
has facts
contains formulation op Lineweaver Burk Equation (Uni Uni Reaction without Product - Irreversibility Assumption) ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Irreversibility Assumption) ni
generalized by task op Linear Parameter Estimation of Enzyme Kinetics ni
linearizes task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product - Michaelis Menten Model - Irreversibility Assumption) ni
is linear dp "true"^^boolean

Linear Parameter Estimation (Uni Uni Reaction without Product - Lineweaver Burk Model - Rapid Equilibrium Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearParameterEstimationUniUniReactionWithoutProductLBRapidEquilibrium

linear fit to determine the limiting reaction rate and michaelis constant
belongs to
Computational Task c
has facts
contains formulation op Lineweaver Burk Equation (Uni Uni Reaction without Product - Rapid Equilibrium Assumption) ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Rapid Equilibrium Assumption) ni
generalized by task op Linear Parameter Estimation of Enzyme Kinetics ni
linearizes task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product - Michaelis Menten Model - Rapid Equilibrium Assumption) ni
is linear dp "true"^^boolean

Linear Parameter Estimation (Uni Uni Reaction without Product - Lineweaver Burk Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearParameterEstimationUniUniReactionWithoutProductLBSteadyState

linear fit to determine the limiting reaction rate and michaelis constant
belongs to
Computational Task c
has facts
contains formulation op Lineweaver Burk Equation (Uni Uni Reaction without Product - Steady State Assumption) ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
generalized by task op Linear Parameter Estimation of Enzyme Kinetics ni
linearizes task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product - Michaelis Menten Model - Steady State Assumption) ni
is linear dp "true"^^boolean

Linear Parameter Estimation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Dixon Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearParameterEstimationUniUniReactionwithoutProductandCompetitiveCompleteInhibitionDixonModelSteadyStateAssumption

linear fit to determine the limiting reaction rate, michaelis constant and inhibition constants
belongs to
Computational Task c
has facts
contains formulation op Dixon Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption) ni
contains input op Inhibitor Concentration ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
generalized by task op Linear Parameter Estimation of Enzyme Kinetics ni
linearizes task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Michaelis Menten Model - Steady State Assumption) ni
is linear dp "true"^^boolean

Linear Parameter Estimation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Eadie Hofstee Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearParameterEstimationUniUniReactionwithoutProductandCompetitiveCompleteInhibitionEadieHofsteeModelSteadyStateAssumption

linear fit to determine the limiting reaction rate, michaelis constant and inhibition constants
belongs to
Computational Task c
has facts
contains formulation op Eadie Hofstee Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption) ni
contains input op Inhibitor Concentration ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
generalized by task op Linear Parameter Estimation of Enzyme Kinetics ni
linearizes task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Michaelis Menten Model - Steady State Assumption) ni
is linear dp "true"^^boolean

Linear Parameter Estimation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Hanes Woolf Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearParameterEstimationUniUniReactionwithoutProductandCompetitiveCompleteInhibitionHanesWoolfModelSteadyStateAssumption

linear fit to determine the limiting reaction rate, michaelis constant and inhibition constants
belongs to
Computational Task c
has facts
contains formulation op Hanes Woolf Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption) ni
contains input op Inhibitor Concentration ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
generalized by task op Linear Parameter Estimation of Enzyme Kinetics ni
linearizes task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Michaelis Menten Model - Steady State Assumption) ni
is linear dp "true"^^boolean

Linear Parameter Estimation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Lineweaver Burk Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearParameterEstimationUniUniReactionwithoutProductandCompetitiveCompleteInhibitionLineweaverBurkModelSteadyStateAssumption

linear fit to determine the limiting reaction rate, michaelis constant and inhibition constants
belongs to
Computational Task c
has facts
contains formulation op Lineweaver Burk Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption) ni
contains input op Inhibitor Concentration ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
generalized by task op Linear Parameter Estimation of Enzyme Kinetics ni
linearizes task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Michaelis Menten Model - Steady State Assumption) ni
is linear dp "true"^^boolean

Linear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Dixon Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearParameterEstimationUniUniReactionwithoutProductandUncompetitiveCompleteInhibitionDixonModelSteadyStateAssumption

linear fit to determine the limiting reaction rate, michaelis constant and inhibition constants
belongs to
Computational Task c
has facts
contains formulation op Dixon Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption) ni
contains input op Inhibitor Concentration ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains output op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
generalized by task op Linear Parameter Estimation of Enzyme Kinetics ni
linearizes task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Michaelis Menten Model - Steady State Assumption) ni
is linear dp "true"^^boolean

Linear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Eadie Hofstee Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearParameterEstimationUniUniReactionwithoutProductandUncompetitiveCompleteInhibitionEadieHofsteeModelSteadyStateAssumption

linear fit to determine the limiting reaction rate, michaelis constant and inhibition constants
belongs to
Computational Task c
has facts
contains formulation op Eadie Hofstee Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption) ni
contains input op Inhibitor Concentration ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains output op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
generalized by task op Linear Parameter Estimation of Enzyme Kinetics ni
linearizes task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Michaelis Menten Model - Steady State Assumption) ni
is linear dp "true"^^boolean

Linear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Hanes Woolf Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearParameterEstimationUniUniReactionwithoutProductandUncompetitiveCompleteInhibitionHanesWoolfModelSteadyStateAssumption

linear fit to determine the limiting reaction rate, michaelis constant and inhibition constants
belongs to
Computational Task c
has facts
contains formulation op Hanes Woolf Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption) ni
contains input op Inhibitor Concentration ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains output op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
generalized by task op Linear Parameter Estimation of Enzyme Kinetics ni
linearizes task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Michaelis Menten Model - Steady State Assumption) ni
is linear dp "true"^^boolean

Linear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Lineweaver Burk Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearParameterEstimationUniUniReactionwithoutProductandUncompetitiveCompleteInhibitionLineweaverBurkModelSteadyStateAssumption

linear fit to determine the limiting reaction rate, michaelis constant and inhibition constants
belongs to
Computational Task c
has facts
contains formulation op Lineweaver Burk Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption) ni
contains input op Inhibitor Concentration ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains output op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
generalized by task op Linear Parameter Estimation of Enzyme Kinetics ni
linearizes task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Michaelis Menten Model - Steady State Assumption) ni
is linear dp "true"^^boolean

Linear Parameter Estimation of Enzyme Kineticsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ParameterEstimationOfEnzymeKineticsLinear

Linear Determination of the Kinetic Constants for Enzyme-catalyzed Reactions.
belongs to
Computational Task c
has facts
doi I D ap B978 0 12 801238 3.05143 6 ep

Linear Rotorni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearRotor

belongs to
Mathematical Model c
has facts
applied by task op Quantum Stationary States ni
applied by task op Quantum Time Evolution ni
approximates model op Linear Rotor (Non-Rigid) ni
contains formulation op Quantum Hamiltonian (Linear Rotor) ni
generalizes model op Linear Rotor (Apolar) ni
generalizes model op Linear Rotor (Polar) ni
description ap "mathematical model of a linear molecule as a rigid rotor"@en

Linear Rotor (Apolar)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearRotorApolar

belongs to
Mathematical Model c
has facts
applied by task op Optimal Control ni
applied by task op Quantum Stationary States ni
applied by task op Quantum Time Evolution ni
contains formulation op Molecular Alignment ni
contains formulation op Molecular Orientation ni
contains formulation op Quantum Hamiltonian (Electric Polarizability) ni
contains formulation op Quantum Hamiltonian (Linear Rotor) ni
generalized by model op Linear Rotor (Combined) ni
description ap "mathematical model of an apolar linear molecule as a rigid rotor, interacting through its induced dipole moment with electric fields"@en

Linear Rotor (Combined)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearRotorCombined

Note that analytical solutions to the TISE are available
belongs to
Mathematical Model c
has facts
applied by task op Optimal Control ni
applied by task op Quantum Conditional Quasi-Solvability ni
applied by task op Quantum Stationary States ni
applied by task op Quantum Time Evolution ni
contains formulation op Molecular Alignment ni
contains formulation op Molecular Orientation ni
contains formulation op Quantum Hamiltonian (Electric Dipole) ni
contains formulation op Quantum Hamiltonian (Electric Polarizability) ni
contains formulation op Quantum Hamiltonian (Linear Rotor) ni
description ap "mathematical model of a polar linear molecule as a rigid rotor, interacting through both its permanent and induced electric dipole moment with electric fields"@en

Linear Rotor (Non-Rigid)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearRotorNonRigid

belongs to
Mathematical Model c
has facts
applied by task op Quantum Stationary States ni
applied by task op Quantum Time Evolution ni
contains formulation op Quantum Hamiltonian (Non-Rigid Rotor) ni
description ap "Modeling a linear molecule as a non-rigid rotor, i.e., the bond between the atoms stretches out as the molecule rotates faster"@en

Linear Rotor (Polar)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearRotorPolar

belongs to
Mathematical Model c
has facts
applied by task op Optimal Control ni
applied by task op Quantum Stationary States ni
applied by task op Quantum Time Evolution ni
contains formulation op Molecular Alignment ni
contains formulation op Molecular Orientation ni
contains formulation op Quantum Hamiltonian (Electric Dipole) ni
contains formulation op Quantum Hamiltonian (Linear Rotor) ni
generalized by model op Linear Rotor (Combined) ni
description ap "mathematical model of a polar linear molecule as a rigid rotor, interacting through its permanent dipole moment with electric fields"@en

Linear Strainni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearStrain

belongs to
Quantity c
has facts
generalized by quantity op Mechanical Strain ni
is dimensionless dp "true"^^boolean
description ap "relative change of length with respect the original length"@en
qudt I D ap Linear Strain ep
wikidata I D ap Q1990546 ep

Linear Strain (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinearStrainDefinition

belongs to
Mathematical Formulation c
has facts
contains quantity op Change In Length ni
contains quantity op Length ni
contains quantity op Linear Strain ni
defines op Linear Strain ni
defining formulation dp "$\varepsilon \equiv \frac{\Delta l}{l}$"^^La Te X ep
in defining formulation dp "$\Delta l$, Change In Length"^^La Te X ep
in defining formulation dp "$\varepsilon$, Linear Strain"^^La Te X ep
in defining formulation dp "$l$, Length"^^La Te X ep
description ap "relative change of length with respect the original length"@en

Lineweaver (1934) The Determination of Enzyme Dissociation Constantsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Lineweaver_1934_The_Determination_of_Enzyme_Dissociation_Constants

belongs to
Publication c
has facts
invents op Uni Uni Reaction (Lineweaver Burk Model without Product - Irreversibility Assumption) ni
invents op Uni Uni Reaction (Lineweaver Burk Model without Product - Rapid Equilibrium Assumption) ni
invents op Uni Uni Reaction (Lineweaver Burk Model without Product - Steady State Assumption) ni
doi I D ap ja01318a036 ep

Lineweaver Burk Equation (Uni Uni Reaction without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LineweaverBurkEquationforUniUniReactionwithoutProductSteadyStateAssumption

Lineweaver Burk Equation for Uni Uni Reaction without Product following Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product - Steady State Assumption) ni
defining formulation dp "$\frac{1}{v_0} = \frac{1}{V_{max,f}} + \frac{K_S}{V_{max,f}} * \frac{1}{c_S}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Lineweaver Burk Equation (Uni Uni Reaction without Product - Irreversibility Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LineweaverBurkEquationforUniUniReactionwithoutProductIrreversibilityAssumption

Lineweaver Burk Equation for Uni Uni Reaction without Product following Irreversibility Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Irreversibility Assumption) ni
contains quantity op Substrate Concentration ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product - Irreversibility Assumption) ni
defining formulation dp "$\frac{1}{v_0} = \frac{1}{V_{max,f}} + \frac{K_S}{V_{max,f}} * \frac{1}{c_S}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Irreversibility Assumption)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Lineweaver Burk Equation (Uni Uni Reaction without Product - Rapid Equilibrium Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LineweaverBurkEquationforUniUniReactionwithoutProductRapidEquilibriumAssumption

Lineweaver Burk Equation for Uni Uni Reaction without Product following Rapid Equilibrium Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Rapid Equilibrium Assumption) ni
contains quantity op Substrate Concentration ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product - Rapid Equilibrium Assumption) ni
defining formulation dp "$\frac{1}{v_0} = \frac{1}{V_{max,f}} + \frac{K_S}{V_{max,f}} * \frac{1}{c_S}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Rapid Equilibrium Assumption)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Lineweaver Burk Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LineweaverBurkEquationUniUniReactionwithoutProductandCompetitiveCompleteInhibitionSteadyStateAssumption

Lineweaver Burk Equation for Uni Uni Reaction without Product and competitive complete Inhibition following Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption) ni
defining formulation dp "$\frac{1}{v_0} = \frac{1}{V_{max,f}} + \frac{K_S * (1 + \frac{c_I}{K_{ic}})}{V_{max,f} * c_S}$"^^La Te X ep
in defining formulation dp "$K_S$,Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{ic}$,Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$,Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$,Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$,Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$,Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Lineweaver Burk Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LineweaverBurkEquationUniUniReactionwithoutProductandMixedCompleteInhibitionSteadyStateAssumption

Lineweaver Burk Equation for Uni Uni Reaction without Product and mixed complete Inhibition following Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni
defining formulation dp "$\frac{1}{v_0} = \frac{1 + \frac{c_I}{K_{iu}}}{V_{max,f}}+ \frac{K_m * (1 + \frac{c_I}{K_{ic}})}{V_{max,f} * c_S}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{ic}$, Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$K_{iu}$, Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$, Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Lineweaver Burk Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LineweaverBurkEquationUniUniReactionwithoutProductandNonCompetitiveCompleteInhibitionSteadyStateAssumption

Lineweaver Burk Equation for Uni Uni Reaction without Product and non-competitive complete Inhibition following Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption) ni
similar to formulation op Lineweaver Burk Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni
defining formulation dp "$\frac{1}{v_0} = \frac{1 + \frac{c_I}{K_{iu}}}{V_{max,f}}+ \frac{K_m * (1 + \frac{c_I}{K_{ic}})}{V_{max,f} * c_S}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{ic}$, Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$K_{iu}$, Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$, Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Lineweaver Burk Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LineweaverBurkEquationUniUniReactionwithoutProductandUncompetitiveCompleteInhibitionSteadyStateAssumption

Lineweaver Burk Equation for Uni Uni Reaction without Product and uncompetitive complete Inhibition following Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
linearizes formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption) ni
defining formulation dp "$\frac{1}{v_0} = \frac{1 + \frac{c_I}{K_{iu}}}{V_{max,f}} + \frac{K_S}{V_{max,f} * c_S}$"^^La Te X ep
in defining formulation dp "$K_S$,Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{iu}$,Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$,Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$,Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$,Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$,Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean

Link Recommendation Functionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LinkRecommendationFunction

Link recommendation algorithms are often used to suggest new connections to users that have the greatest potential to be established. In modelling Opinion Dynamics, link recommendation can be incorporated via this function by assuming that individuals have a higher chance of switching to an influencer with a structurally similar followership. Strictly increasing on [0,1]
belongs to
Quantity c
has facts
description ap "function representing link recommendation"@en

Liouville-von Neumann Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LiouvilleVonNeumannEquation

belongs to
Mathematical Formulation c
is same as
Quantum Liouville Equation ni
has facts
same As ep Quantum Liouville Equation ni
contains quantity op Planck Constant ni
contains quantity op Quantum Density Operator ni
contains quantity op Quantum Hamiltonian Operator ni
contains quantity op Time ni
defining formulation dp "$\frac{\partial\hat\rho}{\partial t} = -\frac{i}{\hbar}\left[\hat H, \hat\rho\right]$"^^La Te X ep
in defining formulation dp "$\hat{H}$, Quantum Hamiltonian Operator"^^La Te X ep
in defining formulation dp "$\hat{\rho}$, Quantum Density Operator"^^La Te X ep
in defining formulation dp "$\hbar$, Planck Constant"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
description ap "describes how a density operator (for pure or for mixed states) evolves in time"@en

Logical Rule Extraction Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LogicalRuleExtractionFormulation

equation that extracts logical rules by determining the Gröbner basis of an ideal
belongs to
Mathematical Formulation c
has facts
contains quantity op Boolean Ring ni
contains quantity op Gröbner Basis ni
contains quantity op Ideal ni
defining formulation dp "$G = G(\langle\mathcal{B}\rangle)$"^^La Te X ep
in defining formulation dp "$G$, Gröbner Basis"^^La Te X ep
in defining formulation dp "$\langle\mathcal{B}\rangle$, Ideal"^^La Te X ep
in defining formulation dp "$\mathcal{B}$, Boolean Ring"^^La Te X ep
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Lorentz Force Equation (Non-Relativistic)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LorentzForceEquationNonRelativistic

belongs to
Mathematical Formulation c
has facts
contains quantity op Classical Force ni
contains quantity op Classical Velocity ni
contains quantity op Electric Charge ni
contains quantity op Electric Field ni
contains quantity op Magnetic Field ni
defining formulation dp "$\boldsymbol{F} = q (\boldsymbol{E} + \boldsymbol{v} \times \boldsymbol{B})$"^^La Te X ep
in defining formulation dp "$B$, Magnetic Field"^^La Te X ep
in defining formulation dp "$E$, Electric Field"^^La Te X ep
in defining formulation dp "$F$, Classical Force"^^La Te X ep
in defining formulation dp "$q$, Electric Charge"^^La Te X ep
in defining formulation dp "$v$, Classical Velocity"^^La Te X ep
description ap "force exerted on a moving electric (point) charge in electromagnetic field (non-relativistic approach)"@en
wikidata I D ap Q172137 ep

Lorentz Force Equation (Relativistic)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LorentzForceEquationRelativistic

belongs to
Mathematical Formulation c
has facts
contains quantity op Classical Velocity ni
contains quantity op Electric Charge ni
contains quantity op Electric Field ni
contains quantity op Magnetic Field ni
contains quantity op Mass ni
contains quantity op Speed Of Light ni
contains quantity op Time ni
generalizes formulation op Lorentz Force Equation (Non-Relativistic) ni
defining formulation dp "$\frac{\mathrm{d} }{\mathrm{d}t} {m\mathbf{v} \over \sqrt{1-\left(\frac{\mathbf{v} }{c}\right)^2} } = q\left ( \mathbf{E} + \mathbf{v} \times \mathbf{B} \right ) $"^^La Te X ep
in defining formulation dp "$B$, Magnetic Field"^^La Te X ep
in defining formulation dp "$E$, Electric Field"^^La Te X ep
in defining formulation dp "$c$, Speed of Light"^^La Te X ep
in defining formulation dp "$m$, Mass"^^La Te X ep
in defining formulation dp "$q$, Electric Charge"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$v$, Classical Velocity"^^La Te X ep
description ap "force exerted on a moving electric (point) charge in electromagnetic field (relativistic approach)"@en
wikidata I D ap Q172137 ep

Lorentz Force Model (Non-Relativistic)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LorentzForceModelNonRelativistic

Neglecting the fact that real particles would generate their own E and B fields, which would alter the electromagnetic forces that they experience.
belongs to
Mathematical Model c
has facts
contains assumption op Classical Approximation ni
contains formulation op Lorentz Force Equation (Non-Relativistic) ni
models op Particles In Electromagnetic Fields ni
description ap "modeling the motion of "test charges" in electromagnetic fields in terms of the Lorentz force"@en
wikidata I D ap Q172137 ep

Lorentz Force Model (Relativistic)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LorentzForceModelRelativistic

Neglecting the fact that real particles would generate their own E and B fields, which would alter the electromagnetic forces that they experience.
belongs to
Mathematical Model c
has facts
contains assumption op Classical Approximation ni
contains formulation op Lorentz Force Equation (Relativistic) ni
generalizes model op Lorentz Force Model (Non-Relativistic) ni
models op Particles In Electromagnetic Fields ni
description ap "modeling the motion of "test charges" in electromagnetic fields in terms of the Lorentz force"@en
wikidata I D ap Q172137 ep

Loss Functionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LossFunction

belongs to
Quantity c
has facts
defined by op Loss Function (Definition) ni
is dimensionless dp "true"^^boolean
description ap "loss function summing over regions and data points"@en
wikidata I D ap Q1036748 ep

Loss Functionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Loss_Function

belongs to
Mathematical Model c
has facts
contained in model op Artificial Neural Network ni
description ap "in mathematical optimization, a function (to be minimized) representing the cost of each outcome"@en
wikidata I D ap Q1036748 ep

Loss Function (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LossFunctionDefinition

belongs to
Mathematical Formulation c
has facts
contains quantity op Spreading Curve (Approximate) ni
contains quantity op Loss Function ni
contains quantity op Number of Regions ni
contains quantity op Number of Time Points ni
contains quantity op Romanized Cities Vector ni
contains quantity op Contact Network (Time-dependent) ni
contains quantity op Time Point ni
contains quantity op Weight Factor ni
defining formulation dp "$\ell (\sigma ) := \sum _{i=1}^{N_T} \sum _{m=1}^{N_R} \frac{(\omega _{m,t_i} - \phi (t_i| \sigma , \omega _{\bullet , 0}))^2 }{C_{m,t_i}^2}$"^^La Te X ep
in defining formulation dp "$C$, Weight Factor"^^La Te X ep
in defining formulation dp "$N_R$, Number of Regions"^^La Te X ep
in defining formulation dp "$N_T$, Number of Time Points"^^La Te X ep
in defining formulation dp "$\ell$, Loss Function"^^La Te X ep
in defining formulation dp "$\omega$, Romanized Cities Vector"^^La Te X ep
in defining formulation dp "$\phi$, Spreading Curve (Approximate)"^^La Te X ep
in defining formulation dp "$\sigma$, Contact Network (Time-dependent)"^^La Te X ep
in defining formulation dp "$t_i$, Time Point"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean
is dynamic dp "false"^^boolean
description ap "loss function summing over regions and data points"@en

Loss Function Minimizationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LossFunctionMinimization

belongs to
Mathematical Formulation c
has facts
contains quantity op Contact Network ni
contains quantity op Loss Function ni
contains quantity op Contact Network (Time-dependent) ni
defining formulation dp "$\min _{\sigma =(G, \alpha )} \ell (\sigma )$"^^La Te X ep
in defining formulation dp "$G$, Contact Network"^^La Te X ep
in defining formulation dp "$\ell$, Loss Function"^^La Te X ep
in defining formulation dp "$\sigma$, Contact Network (Time-dependent)"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean
is dynamic dp "false"^^boolean
description ap "minimization of loss function over regions and data points"@en

Lumped Activation Parameterni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LumpedActivationParameter

belongs to
Mathematical Formulation c
has facts
contains quantity op Fiber Contraction Velocity ni
contains quantity op Fiber Stretch ni
defining formulation dp "$\gamma = H \left( \mathbf{y}, \lambda_\text{f}, \dot{\lambda}_{\text{f}}\right)$"^^La Te X ep
in defining formulation dp "$\dot{\lambda}_{\text{f}}$, Fibre Contraction Velocity"^^La Te X ep
in defining formulation dp "$\lambda_{\text{f}}$, Fibre stretch"^^La Te X ep
in defining formulation dp "$\mathbf{y}$, Vector of internal state variables"^^La Te X ep
description ap "lumped activation parameter"@en

Lyapunov Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LyapunovEquation

Numerical solution of a Lyapunov equation $AX+XA^T+B=0$ via Zhou and Sorensen 2-solve method, implemented as part of the Matrix Equation Sparse Solver (M.E.S.S.) project. Copyright 2009-2022 Jens Saak, Martin Koehler, Peter Benner and others.
belongs to
Mathematical Formulation c
has facts
generalizes formulation op Lyapunov Equation Controllability ni
generalizes formulation op Lyapunov Equation Observability ni
defining formulation dp "$AX+XA^H+Q=0$"^^La Te X ep
in defining formulation dp "$A^H$, the conjugate transpose of A"^^La Te X ep
in defining formulation dp "$Q$, Hermitian matrix"^^La Te X ep
description ap "matrix equation used in the stability analysis of linear dynamical systems"@en
doi I D ap S1110757 X03212055 ep
wikidata I D ap Q1028945 ep

Lyapunov Equation Controllabilityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LyapunovEquationControllability

For the solvability of ordinary Lyapunov equations, the stability condition for A is the only requirement.
belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Matrix A ni
contains quantity op Control System Matrix B ni
contains quantity op Gramian Matrix Controllability ni
similar to formulation op Lyapunov Equation Observability ni
defining formulation dp "$AW_c + W_cA^{*} + BB^{*} = 0$"^^La Te X ep
in defining formulation dp "$A$, Control System Matrix A"^^La Te X ep
in defining formulation dp "$B$, Control System Matrix B"^^La Te X ep
in defining formulation dp "$W_c$, Gramian Matrix Controllability"^^La Te X ep
description ap "Lyapunov equation used in the stability analysis of linear dynamical systems to determine the controllability"@en

Lyapunov Equation Observabilityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LyapunovEquationObservability

For the solvability of ordinary Lyapunov equations, the stability condition for A is the only requirement.
belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Matrix A ni
contains quantity op Control System Matrix C ni
contains quantity op Gramian Matrix Observability ni
defining formulation dp "$A^{*}W_o + W_oA + C^*C = 0$"^^La Te X ep
in defining formulation dp "$A$, Control System Matrix A"^^La Te X ep
in defining formulation dp "$C$, Control System Matrix C"^^La Te X ep
in defining formulation dp "$W_o$, Gramian Matrix Observability"^^La Te X ep
description ap "Lyapunov equation used in the stability analysis of linear dynamical systems to determine the observability"@en

Lyapunov Generalized Controllabilityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LyapunovGeneralizedControllability

For a numerical solution, one can resort to iterative schemes, which requires the solution of a standard Lyapunov equation in each step. As an alternative, one may use the biconjugate gradient method (with preconditioner) as suggested by Tobias Breiten from TU Graz, Austria, now TU Berlin.
belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Matrix A ni
contains quantity op Control System Matrix B ni
contains quantity op Control System Matrix N ni
contains quantity op Gramian Generalized Controllability ni
generalized by formulation op Lyapunov Equation ni
generalizes formulation op Lyapunov Equation Controllability ni
similar to formulation op Lyapunov Generalized Observability ni
defining formulation dp "$AW_c + W_cA^{*} + \sum_kN_kW_{c}N_k^{*} + BB^{*} = 0$"^^La Te X ep
in defining formulation dp "$A$, Control System Matrix A"^^La Te X ep
in defining formulation dp "$B$, Control System Matrix B"^^La Te X ep
in defining formulation dp "$N$, Control System Matrix N"^^La Te X ep
in defining formulation dp "$W_c$, Gramian Generalized Controllability"^^La Te X ep
description ap "generalized Lyapunov equation used in the stability analysis of linear dynamical systems to determine the controllability"@en

Lyapunov Generalized Observabilityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#LyapunovGeneralizedObservability

For a numerical solution, one can resort to iterative schemes, which requires the solution of a standard Lyapunov equation in each step. As an alternative, one may use the biconjugate gradient method (with preconditioner) as suggested by Tobias Breiten from TU Graz, Austria, now TU Berlin.
belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Matrix A ni
contains quantity op Control System Matrix C ni
contains quantity op Control System Matrix N ni
contains quantity op Gramian Generalized Observability ni
generalized by formulation op Lyapunov Equation ni
generalizes formulation op Lyapunov Equation Observability ni
defining formulation dp "$A^{*}W_o + W_oA + \sum_k N_k^{*}W_{o}N_k + C^*C = 0$"^^La Te X ep
in defining formulation dp "$A$, Control System Matrix A"^^La Te X ep
in defining formulation dp "$C$, Control System Matrix C"^^La Te X ep
in defining formulation dp "$N$, Control System Matrix N"^^La Te X ep
in defining formulation dp "$W_c$, Gramian Generalized Observability"^^La Te X ep
description ap "generalized Lyapunov equation used in the stability analysis of linear dynamical systems to determine the observability"@en

Magnetic Constantni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MagneticConstant

belongs to
Quantity c
is same as
Permeability (Vacuum) ni
has facts
same As ep Permeability (Vacuum) ni
description ap "ratio between the magnetic H-field and the magnetic B-field in classical vacuum"@en
qudt I D ap Magnetic Constant ep
wikidata I D ap Q1515261 ep

Magnetic Fieldni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MagneticField

Spatial distribution of vectors allowing the calculation of the magnetic force on a test particle
belongs to
Quantity Kind c
has facts
qudt I D ap Magnetic Field Strength H ep
wikidata I D ap Q11408 ep

Massni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Mass

Property of matter to resist changes of the state of motion and to attract other bodies
belongs to
Quantity Kind c
has facts
contained in formulation op Classical Newton Equation ni
qudt I D ap Mass ep
wikidata I D ap Q11423 ep

Mass Action Lawni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MassActionLaw

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Molecularity ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
defining formulation dp "$v = k * \prod_{i=1}^{n} c_{i}$"^^La Te X ep
in defining formulation dp "$c_i$, Concentration"^^La Te X ep
in defining formulation dp "$k$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$n$, Molecularity"^^La Te X ep
in defining formulation dp "$v$, Reaction Rate"^^La Te X ep
description ap "rate of chemical reaction is directly proportional to the product of the activities or concentrations of the reactants"@en
wikidata I D ap Q899494 ep

Mass Balance Lawni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MassBalanceLaw

belongs to
Mathematical Formulation c
has facts
generalized by formulation op Conservation Law ni
defining formulation dp "$\delta_t + \nabla F = 0$"^^La Te X ep
description ap "mass that enters a system must, by conservation of mass, either leave the system or accumulate within the system"@en
wikidata I D ap Q3276889 ep

Material Densityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MaterialDensity

belongs to
Quantity c
has facts
generalized by quantity op Density ni
description ap "measure of how much mass is contained within a given volume of a material"@en

Material Point Accelerationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MaterialPointAcceleration

belongs to
Quantity c
has facts
generalized by quantity op Acceleration ni
description ap "acceleration experienced by material points in the Material Point Method"@en

Material Point Displacementni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MaterialPointDisplacement

Material Point Displacement in the context of the Material Point Method (MPM) refers to the movement of material points, which are used to track physical information like mass and velocity.
belongs to
Quantity c
has facts
generalized by quantity op Displacement ni
description ap "movement of material points"@en

Material Point Velocityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MaterialPointVelocity

Material Point Velocity in the context of the Material Point Method (MPM) refers to the velocity assigned to each material point within a simulation.
belongs to
Quantity c
has facts
generalized by quantity op Velocity ni
description ap "velocity assigned to each material point within a simulation"@en

Mathematical Analysis of DHW Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MathematicalAnalysisOfDHWEquation

belongs to
Computational Task c
has facts
applies model op Dynamical Electron Scattering Model ni
description ap "mathematical analysis of Darwin Howie Whelan equation for the scattering of fast electrons described by the Schrödinger equation."@en
doi I D ap 21 M139164 X ep

Maximal Object Descriptiveness Ratingni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MaimalObjectDescriptivenessRating

belongs to
Quantity c
has facts
generalized by quantity op Integer Number (Dimensionless) ni
is dimensionless dp "true"^^boolean
description ap "maximal rating assigned to an object commonality in terms of object descriptiveness"@en

Maximizing Poisson log-Likelihoodni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MaximizingPoissonLogLikelihood

belongs to
Computational Task c
has facts
applies model op Gamma-Gompertz-Makeham Model ni
contains formulation op Poisson log-Likelihood ni
contains input op Death Count ni
contains input op Exposure Of An Individual ni
contains output op Extrinsic Mortality ni
contains output op Heterogeneity of Death Rate ni
contains output op Level Of Mortality ni
contains output op Likelihood Value ni
contains output op Rate Of Aging ni
generalized by task op Maximum Likelihood Estimation ni
description ap "maximizing Poisson log-likelihood of mortality models"@en

Maximum Isometric Muscle Forceni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MaximumIsometricMuscleForce

belongs to
Quantity c
has facts
generalized by quantity op Force ni
description ap "greatest force a muscle can generate without changing its length"@en

Maximum Likelihood Estimationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MaximumLikelihoodEstimation

belongs to
Computational Task c
has facts
description ap "estimating the parameters of a statistical model to fit given observations"@en
wikidata I D ap Q1045555 ep

Maxwell Equations Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MaxwellEquationsModel

Shalva: Given the charge density ρ(r, t) and the current density j(r, t), Maxwell's equations yield the electric and magnetic fields, E(r, t) and B(r, t). These equations are the simplest representative of a more general class of models, also referred as Maxwell's equations, where ρ(r, t) and j(r, t) should be found from certain additional relations, e.g., from the Ohm's law.
belongs to
Mathematical Model c
has facts
contains assumption op Classical Approximation ni
contains assumption op Nonrelativistic Approximation ni
description ap "set of four coupled partial differential equations describing how electric and magnetic fields are generated and altered by each other and by charges and currents"@en
doi I D ap rstl.1865.0008 ep
wikidata I D ap Q51501 ep

Mechanical Deformationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MechanicalDeformation

In engineering or in continuum mechanics, any changes in the shape or size of a matter object
belongs to
Quantity Kind c
has facts
wikidata I D ap Q2672013 ep

Mechanical Deformation (Boundary Value)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MechanicalDeformationBoundaryValue

belongs to
Quantity c
has facts
generalized by quantity op Mechanical Deformation ni
description ap "mechanical deformation at a domain boundary"@en

Mechanical Strainni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MechanicalStrain

In continuum mechanics, strain is defined as the relative deformation of matter caused by mechanical stress.
belongs to
Quantity Kind c
has facts
generalizes quantity op Linear Strain ni
nondimensionalizes quantity op Mechanical Deformation ni
qudt I D ap Strain ep
wikidata I D ap Q3083131 ep

Mechanical Stressni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MechanicalStress

Internal forces caused by deformation of a continuous material. Has components shear stress, normal stress. These macroscopic forces are actually the net result of a very large number of intermolecular forces and collisions between the constituent atoms or molecules.
belongs to
Quantity Kind c
has facts
generalizes quantity op Eigenstress Of Crystal ni
generalizes quantity op Fluid Viscous Stress ni
generalizes quantity op Normal Stress ni
generalizes quantity op Stress Of Crystal ni
qudt I D ap Stress ep
wikidata I D ap Q206175 ep

Medical Imagingni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MedicalImaging

belongs to
Research Field c
has facts
description ap "technique and process of creating visual representations of the interior of a body"@en
wikidata I D ap Q931309 ep

Medium Follower Matrixni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MediumFollowerMatrix

$\{0, 1\}^{N\times M}$ Binary adjacency Matrix for medium-follower relations. we store which individual follows which medium at time t
belongs to
Quantity c
has facts
description ap "adjacency matrix for medium-follower relations at time t"@en

Medium Influencer Fractionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MediumInfluencerFraction

Fraction of individuals that follow a specific medium and influencer at a given time. Superscript N denotes the number of Individuals
belongs to
Quantity c
has facts
description ap "fraction of individuals following a specific medium and influencer at a given time"@en

Medium Influencer Fraction Limitni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MediumInfluencerFractionLimit

belongs to
Quantity c
has facts
generalized by op Medium Influencer Fraction ni
description ap "fraction of individuals following a specific medium and influencer at a given time with total number of Individuals tending to infinity"@en

Membrane Capacitanceni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MembraneCapacitance

belongs to
Quantity c
has facts
generalized by quantity op Electric Capacitance ni
description ap "how much charge a cell membrane can store when a voltage is applied across it"@en

Membrane Potentialni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MembranePotential

belongs to
Quantity c
is same as
Transmembrane Potential ni
has facts
same As ep Transmembrane Potential ni
generalized by quantity op Electric Potential ni
description ap "difference of the electric potential between the inner and the outer part of a biological cell"@en
alt Label ap "Membrane Voltage"@en
alt Label ap "Transmembrane Potential"@en
wikidata I D ap Q389844 ep

Michaelis (1913) Die Kinetik der Invertinwirkungni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Michaelis_1913_Die_Kinetik_der_Invertinwirkung

belongs to
Publication c
has facts
invents op Uni Uni Reaction (Michaelis Menten Model without Product - Rapid Equilibrium Assumption) ni

Michaelis Constantni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisConstant

Property to characterize the kinetics of Michaelis–Menten reactions
belongs to
Quantity c
has facts
description ap "property to characterize the kinetics of Michaelis–Menten reactions"@en
wikidata I D ap Q61751178 ep

Michaelis Constant Product (Uni Uni Reaction - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisConstantProductUniUniReactionSteadyStateAssumption

belongs to
Quantity c
has facts
defined by op Michaelis Constant Product (Uni Uni Reaction - Steady State Assumption, Definition) ni
generalized by quantity op Concentration ni
generalized by quantity op Michaelis Constant ni
is dimensionless dp "false"^^boolean
description ap "Michaelis constant for the product of an Uni Uni Reaction under the Steady State Assumption"@en

Michaelis Constant Product (Uni Uni Reaction - Steady State Assumption, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisConstantProductUniUniReactionSteadyStateAssumptionDefinition

Definition of Michaelis constant for the product on an Uni Uni Reaction under the Staedy State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant Product (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{P} \equiv \frac{k_{-1} + k_{2}}{k_{-2}}$"^^La Te X ep
in defining formulation dp "$K_{P}$, Michaelis Constant Product (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean

Michaelis Constant Product 1 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenConstantProduct1BiBiReactionOrderedsingleCCSS

belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{P_1} = \frac{k_{-1} * k_{-2}}{k_{-5} * (k_{-1} + k_{-2})}$"^^La Te X ep
in defining formulation dp "$K_{P_1}}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-5}$, Reaction Rate Constant"^^La Te X ep

Michaelis Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisConstantProduct1BiBiReactionOrderedSteadyStateAssumption

belongs to
Quantity c
has facts
defined by op Michaelis Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption, Definition) ni
generalized by quantity op Concentration ni
generalized by quantity op Michaelis Constant ni
is dimensionless dp "false"^^boolean
description ap "Michaelis constant for the product 1 of a Bi Bi Reaction with Ordered Mechanism under the Steady State Assumption"@en

Michaelis Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisConstantProduct1BiBiReactionOrderedSteadyStateAssumptionDefinition

Definition of Michaelis constant for the product 1 of a Bi Bi Reaction with Ordered Mechanism under the Staedy State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{P_1} \equiv \frac{k_{-1} * k_{-2} * k_{-3}}{k_{-5} * (k_{-1} * k_{-2} + k_{-1} * k_3 + k_{-1} * k_{-3} + k_{-2} * k_{-3})}$"^^La Te X ep
in defining formulation dp "$K_{P_1}$, Michaelis Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-5}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean

Michaelis Constant Product 1 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenConstantProduct1BiBiReactionPingPongSS

belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{P_1} = \frac{k_{-3} * (k_{-1} + k_{2})}{k_{-2} * (k_{-1} + k_{-3})}$"^^La Te X ep
in defining formulation dp "$K_{P_1}}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep

Michaelis Constant Product 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenConstantProduct1BiBiReactionTheorellChanceSS

belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{P_1} = \frac{k_{-1}}{k_{-2}}$"^^La Te X ep
in defining formulation dp "$K_{P_1}}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep

Michaelis Constant Product 2 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenConstantProduct2BiBiReactionOrderedsingleCCSS

belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{P_2} = \frac{k_{-1} * (k_{-2} + k_4)}{k_{-4} * (k_{-1} + k_{-2})}$"^^La Te X ep
in defining formulation dp "$K_{P_1}}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep

Michaelis Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisConstantProduct2BiBiReactionOrderedSteadyStateAssumption

belongs to
Quantity c
has facts
defined by op Michaelis Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption, Definition) ni
generalized by quantity op Concentration ni
generalized by quantity op Michaelis Constant ni
is dimensionless dp "false"^^boolean
description ap "Michaelis constant for the product 2 of a Bi Bi Reaction with Ordered Mechanism under the Steady State Assumption"@en

Michaelis Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisConstantProduct2BiBiReactionOrderedSteadyStateAssumptionDefinition

Definition of Michaelis constant for the product 2 of a Bi Bi Reaction with Ordered Mechanism under the Staedy State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{P_2} \equiv \frac{k_{-1} * (k_{-2} * k_{4} + k_{-2} * k_{-3} + k_3 * k_4)}{k_{-5} * (k_{-1} * k_{-2} + k_{-1} * k_3 + k_{-1} * k_{-3} + k_{-2} * k_{-3})}$"^^La Te X ep
in defining formulation dp "$K_{P_2}$, Michaelis Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean

Michaelis Constant Product 2 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenConstantProduct2BiBiReactionPingPongSS

belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{P_2} = \frac{k_{-1} * (k_{-3} + k_{4})}{k_{-4} * (k_{-1} + k_{-3})}$"^^La Te X ep
in defining formulation dp "$K_{P_2}}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep

Michaelis Constant Product 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenConstantProduct2BiBiReactionTheorellChanceSS

belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{P_2} = \frac{k_{-1}}{k_{-3}}$"^^La Te X ep
in defining formulation dp "$K_{P_2}}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep

Michaelis Constant Substrate (Uni Uni Reaction - Irreversibility Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisConstantSubstrateUniUniReactionIrreversibilityAssumption

belongs to
Quantity c
has facts
defined by op Michaelis Constant Substrate (Uni Uni Reaction - Irreversibility Assumption, Definition) ni
generalized by quantity op Concentration ni
generalized by quantity op Michaelis Constant ni
is dimensionless dp "false"^^boolean
description ap "Michaelis constant for the substrate of an Uni Uni Reaction under the Irreversibility Assumption"@en

Michaelis Constant Substrate (Uni Uni Reaction - Irreversibility Assumption, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisConstantSubstrateUniUniReactionIrreversibilityAssumptionDefinition

Definition of Michaelis constant for the substrate of an Uni Uni Reaction under the Irreversibility Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Irreversibility Assumption) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{S} \equiv \frac{k_2}{k_{1}}$"^^La Te X ep
in defining formulation dp "$K_{S}$, Michaelis Constant Substrate (Uni Uni Reaction - Irreversibility Assumption)"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean

Michaelis Constant Substrate (Uni Uni Reaction - Rapid Equilibrium Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisConstantSubstrateUniUniReactionRapidEquilibriumAssumption

belongs to
Quantity c
has facts
defined by op Michaelis Constant Substrate (Uni Uni Reaction - Rapid Equilibrium Assumption, Definition) ni
generalized by quantity op Concentration ni
generalized by quantity op Michaelis Constant ni
is dimensionless dp "false"^^boolean
description ap "Michaelis constant for the substrate of an Uni Uni Reaction under the Rapid Equilibrium Assumption"@en

Michaelis Constant Substrate (Uni Uni Reaction - Rapid Equilibrium Assumption, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisConstantSubstrateUniUniReactionRapidEquilibriumAssumptionDefinition

Definition of Michaelis constant for the substrate of an Uni Uni Reaction under the Rapid Equilibrium Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Rapid Equilibrium Assumption) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{S} \equiv \frac{k_{-1}}{k_{1}}$"^^La Te X ep
in defining formulation dp "$K_{S}$, Michaelis Constant Substrate (Uni Uni Reaction - Rapid Equilibrium Assumption)"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean

Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisConstantSubstrateUniUniReactionSteadyStateAssumption

belongs to
Quantity c
has facts
defined by op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption, Definition) ni
generalized by quantity op Concentration ni
generalized by quantity op Michaelis Constant ni
is dimensionless dp "false"^^boolean
description ap "Michaelis constant for the substrate of an Uni Uni Reaction under the Staedy State Assumption"@en

Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisConstantSubstrateUniUniReactionSteadyStateAssumptionDefinition

Definition of Michaelis constant for the substrate of an Uni Uni Reaction under the Staedy State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{S} \equiv \frac{k_{-1} + k_{2}}{k_{1}}$"^^La Te X ep
in defining formulation dp "$K_{S}$, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean

Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisConstantSubstrate1BiBiReactionOrderedSteadyStateAssumption

Michaelis constant for the substrate 1 of a Bi Bi Reaction with Ordered Mechanism under the Steady State Assumption
belongs to
Quantity c
has facts
defined by op Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption, Definition) ni
generalized by quantity op Concentration ni
generalized by quantity op Michaelis Constant ni
is dimensionless dp "false"^^boolean

Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisConstantSubstrate1BiBiReactionOrderedSteadyStateAssumptionDefinition

Definition of Michaelis constant for the substrate 1 of a Bi Bi Reaction with Ordered Mechanism under the Staedy State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{S_1} \equiv \frac{k_3 * k_4 * k_5}{k_1 * (k_4 * k_5 + k_3 * k_4 + k_3 * k_5 + k_{-3} * k_5)}$"^^La Te X ep
in defining formulation dp "$K_{S_1}$, Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{5}$, Reaction Rate Constant"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean

Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenConstantSubstrate1BiBiReactionOrderedsingleCCSS

belongs to
Quantity c
has facts
defined by op Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption, Definition) ni
generalized by quantity op Concentration ni
generalized by quantity op Michaelis Constant ni
is dimensionless dp "false"^^boolean
description ap "Michaelis constant for the substrate 1 of a Bi Bi Reaction with Ordered Mechanism and single central Complex under the Steady State Assumption"@en

Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenConstantSubstrate1BiBiReactionOrderedsingleCCSSDefinition

Definition of Michaelis constant for the substrate 1 of a Bi Bi Reaction with Ordered Mechanism and single central Complex under the Staedy State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{S_1} \equiv \frac{k_4 * k_5}{k_1 * (k_4 + k_5)}$"^^La Te X ep
in defining formulation dp "$K_{S_1}$, Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{5}$, Reaction Rate Constant"^^La Te X ep

Michaelis Constant Substrate 1 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenConstantSubstrate1BiBiReactionPingPongSS

belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{S_1} = \frac{k_{4} * (k_{-1} + k_{2})}{k_{1} * (k_{2} + k_{4})}$"^^La Te X ep
in defining formulation dp "$K_{S_1}}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep

Michaelis Constant Substrate 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenConstantSubstrate1BiBiReactionTheorellChanceSS

belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{S_1} = \frac{k_{3}}{k_{1}}$"^^La Te X ep
in defining formulation dp "$K_{S_1}}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep

Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisConstantSubstrate2BiBiReactionOrderedSteadyStateAssumption

belongs to
Quantity c
has facts
defined by op Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption, Definition) ni
generalized by quantity op Concentration ni
generalized by quantity op Michaelis Constant ni
is dimensionless dp "false"^^boolean
description ap "Michaelis constant for the substrate 2 of a Bi Bi Reaction with Ordered Mechanism under the Staedy State Assumption"@en

Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisConstantSubstrate2BiBiReactionOrderedSteadyStateAssumptionDefinition

Definition of Michaelis constant for the substrate 2 of a Bi Bi Reaction with Ordered Mechanism under the Staedy State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{S_2} \equiv \frac{k_5 * (k_{-2} * k_4 + k_{-2} * k_{-3} + k_3 * k_4)}{k_2 * (k_4 * k_5 + k_3 * k_4 + k_3 * k_5 + k_{-3} * k_5)}$"^^La Te X ep
in defining formulation dp "$K_{S_2}$, Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{5}$, Reaction Rate Constant"^^La Te X ep

Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenConstantSubstrate2BiBiReactionOrderedsingleCCSS

belongs to
Quantity c
has facts
defined by op Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption, Definition) ni
generalized by quantity op Concentration ni
generalized by quantity op Michaelis Constant ni
is dimensionless dp "false"^^boolean
description ap "Michaelis constant for the substrate 2 of a Bi Bi Reaction with Ordered Mechanism and single central Complex under the Staedy State Assumption"@en

Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenConstantSubstrate2BiBiReactionOrderedsingleCCSSDefinition

Definition of Michaelis constant for the substrate 2 of a Bi Bi Reaction with Ordered Mechanism and single central Complex under the Staedy State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption) ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{S_2}} \equiv \frac{k_5 * (k_{-2} + k_4)}{k_2 * (k_4 + k_5)}$"^^La Te X ep
in defining formulation dp "$K_{S_2}}$, Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{5}$, Reaction Rate Constant"^^La Te X ep

Michaelis Constant Substrate 2 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenConstantSubstrate2BiBiReactionPingPongSS

belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{S_2} = \frac{k_{2} * (k_{-3} + k_{4})}{k_{3} * (k_{2} + k_{4})}$"^^La Te X ep
in defining formulation dp "$K_{S_2}}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep

Michaelis Constant Substrate 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenConstantSubstrate2BiBiReactionTheorellChanceSS

belongs to
Mathematical Formulation c
has facts
contains quantity op Michaelis Constant ni
contains quantity op Reaction Rate Constant ni
defining formulation dp "$K_{S_2} = \frac{k_{3}}{k_{2}}$"^^La Te X ep
in defining formulation dp "$K_{S_2}}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep

Michaelis Menten Equation (Bi Bi Reaction Ordered with Product 1 - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationforBiBiReactionOrderedMechanismwithProduct1SS

Michaelis Menten Equation for Bi Bi Reaction with Ordered Mechanism and Product 1 following Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Product 1 (Steady State Assumption) ni
contains quantity op Inhibition Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Forward) ni
contains quantity op Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Product Concentration ni
contains quantity op Substrate Concentration ni
defining formulation dp "$v_0 = \frac{V_{max,f} * c_{S_1} * c_{S_2}}{K_{iS_1} * K_{S_2} + K_{S_2} * c_{S_1} + K_{S_1} * c_{S_2} + \frac{K_{iS_1} * K_{S_2}}{K_{iP_1}} * c_{P_1} + c_{S_1} * c_{S_2} + \frac{K_{S_1}}{K_{iP_1}} * c_{S_2} * c_{P_1}}$"^^La Te X ep
in defining formulation dp "$K_{S_1}$, Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{S_2}$, Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{iP_1}$, Inhibition Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{iS_1}$, Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Forward)"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Product Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Michaelis Menten Equation (Bi Bi Reaction Ordered with Product 1 and single central Complex - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationforBiBiReactionOrderedMechanismwithProduct1SingleCCSS

Michaelis Menten Equation for Bi Bi Reaction with Ordered Mechanism and Product 1 and single central Complex following Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Product 1 and single central Complex (Steady State Assumption) ni
contains formulation op Inhibition Constant Product 1 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni
contains quantity op Inhibition Constant ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism with single central Complex - Forward) ni
contains quantity op Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption) ni
contains quantity op Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption) ni
contains quantity op Product Concentration ni
contains quantity op Substrate Concentration ni
defining formulation dp "$v_0 = \frac{V_{max,f} * c_{S_1} * c_{S_2}}{K_{iS_1} * K_{S_2} + K_{S_2} * c_{S_1} + K_{S_1} * c_{S_2} + \frac{K_{iS_1} * K_{S_2}}{K_{iP_1}} * c_{P_1} + c_{S_1} * c_{S_2} + \frac{K_{S_1}}{K_{iP_1}} * c_{S_2} * c_{P_1}}$"^^La Te X ep
in defining formulation dp "$K_{S_1}$, Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{S_2}$, Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{iP_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$K_{iS_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Product Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Michaelis Menten Equation (Bi Bi Reaction Ordered with Product 2 - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationforBiBiReactionOrderedMechanismwithProduct2SS

Michaelis Menten Equation for Bi Bi Reaction with Ordered Mechanism and Product 2 following Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibition Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Inhibition Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Forward) ni
contains quantity op Michaelis Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Michaelis Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Product Concentration ni
contains quantity op Substrate Concentration ni
defining formulation dp "$v_0 = \frac{V_{max,f} * c_{S_1} * c_{S_2}}{K_{iS_1} * K_{S_2} + K_{S_2} * c_{S_1} + K_{S_1} * c_{S_2} + \frac{K_{iS_1} * K_{S_2} * K_{P_1}}{K_{iP_1} * K_{P_2}} * c_{P_2} + c_{S_1} * c_{S_2} + \frac{K_{S_2} * K_{P_1}}{K_{iP_1} * K_{P_2}} * c_{S_1} * c_{P_2} + \frac{1}{K_{iP_2}} * c_{S_1} * c_{S_2} * c_{P_2}}$"^^La Te X ep
in defining formulation dp "$K_{P_1}$, Michaelis Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{P_2}$, Michaelis Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{S_1}$, Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{S_2}$, Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{iP_1}$, Inhibition Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{iP_2}$, Inhibition Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{iS_1}$, Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Forward)"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Product Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Michaelis Menten Equation (Bi Bi Reaction Ordered with Product 2 and single central Complex - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationforBiBiReactionOrderedMechanismwithProduct2SingleCCSS

Michaelis Menten Equation for Bi Bi Reaction with Ordered Mechanism and Product 2 and single central Complex following Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contains formulation op Inhibition Constant Product 1 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Inhibition Constant Product 2 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Product 1 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Product 2 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni
contains quantity op Inhibition Constant ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism with single central Complex - Forward) ni
contains quantity op Michaelis Constant ni
contains quantity op Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption) ni
contains quantity op Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption) ni
contains quantity op Product Concentration ni
contains quantity op Substrate Concentration ni
defining formulation dp "$v_0 = \frac{V_{max,f} * c_{S_1} * c_{S_2}}{K_{iS_1} * K_{S_2} + K_{S_2} * c_{S_1} + K_{S_1} * c_{S_2} + \frac{K_{iS_1} * K_{S_2} * K_{P_1}}{K_{iP_1} * K_{P_2}} * c_{P_2} + c_{S_1} * c_{S_2} + \frac{K_{S_2} * K_{P_1}}{K_{iP_1} * K_{P_2}} * c_{S_1} * c_{P_2} + \frac{1}{K_{iP_2}} * c_{S_1} * c_{S_2} * c_{P_2}}$"^^La Te X ep
in defining formulation dp "$K_{P_1}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{P_2}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{S_1}$, Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{S_2}$, Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{iP_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$K_{iP_2}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$K_{iS_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Product Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Michaelis Menten Equation (Bi Bi Reaction Ordered with Products 1 and 2 - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationforBiBiReactionOrderedMechanismwithProducts1and2SS

Michaelis Menten Equation for Bi Bi Reaction with Ordered Mechanism and Products 1 and 2 following Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Products 1 and 2 (Steady State Assumption) ni
contains quantity op Equilibrium Constant (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Inhibition Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Inhibition Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Inhibition Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Backward) ni
contains quantity op Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Forward) ni
contains quantity op Michaelis Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Michaelis Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Product Concentration ni
contains quantity op Substrate Concentration ni
defining formulation dp "$v_0 = \frac{V_{max,f} * V_{max,b} * (c_{S_1} * c_{S_2} - \frac{c_{P_1} * c_{P_2}}{K_{eq}})}{V_{max,b} * K_{iS_1} * K_{S_2} + V_{max,b} * K_{S_2} * c_{S_1} + V_{max,b} * K_{S_1} * c_{S_2} + \frac{V_{max,f} * K_{P_1}}{K_{eq}} * c_{P_2} + \frac{V_{max,f} * K_{P_2}}{K_{eq}} * c_{P_1} + V_{max,b} * c_{S_1} * c_{S_2} + \frac{V_{max,f} * K_{P_1}}{K_{iS_1} * K_{eq}} * c_{S_1} * c_{P_2} + \frac{V_{max,f}}{K_{eq}} * c_{P_1} * c_{P_2} + \frac{V_{max,b} * K_{S_1}}{K_{iP_1}} * c_{S_1} * c_{P_1} + \frac{V_{max,b}}{K_{iP_2}} * c_{S_1} * c_{S_2} * c_{P_2} + \frac{V_{max,f}}{K_{iS_2} * K_{eq}} * c_{S_2} * c_{P_1} * c_{P_2}}$"^^La Te X ep
in defining formulation dp "$K_{P_1}$, Michaelis Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{P_2}$, Michaelis Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{S_1}$, Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{S_2}$, Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{eq}$, Equilibrium Constant (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{iP_1}$, Inhibition Constant Product 1 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{iP_2}$, Inhibition Constant Product 2 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{iS_1}$, Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{iS_2}$, Inhibition Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$V_{max,b}$, Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Backward)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Forward)"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Product Concentration"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Product Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Michaelis Menten Equation (Bi Bi Reaction Ordered with Products 1 and 2 and single central Complex - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationforBiBiReactionOrderedMechanismwithProducts1and2SingleCCSS

Michaelis Menten Equation for Bi Bi Reaction with Ordered Mechanism and Products 1 and 2 and single central Complex following Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Products 1 and 2 and single central Complex (Steady State Assumption) ni
contains formulation op Equilibrium Constant (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Inhibition Constant Product 1 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Inhibition Constant Product 2 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Inhibition Constant Substrate 2 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Limiting Reaction Rate Backward (Bi Bi Reaction Ordered - Single central Complex) ni
contains formulation op Michaelis Constant Product 1 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Product 2 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni
contains quantity op Concentration ni
contains quantity op Equilibrium Constant ni
contains quantity op Inhibition Constant ni
contains quantity op Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism with single central Complex - Forward) ni
contains quantity op Michaelis Constant ni
contains quantity op Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption) ni
contains quantity op Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption) ni
contains quantity op Reaction Rate ni
defining formulation dp "$v_0 = \frac{V_1 * V_2 * (c_{S_1} * c_{S_2} - \frac{c_{P_1} * c_{P_2}}{K_{eq}})}{V_2 * K_{iS_1} * K_{S_2} + V_2 * K_{S_2} * c_{S_1} + V_2 * K_{S_1} * c_{S_2} + \frac{V_1 * K_{P_1}}{K_{eq}} * c_{P_2} + \frac{V_1 * K_{P_2}}{K_{eq}} * c_{P_1} + V_2 * c_{S_1} * c_{S_2} + \frac{V_1 * K_{P_1}}{K_{iS_1} * K_{eq}} * c_{S_1} * c_{P_2} + \frac{V_1}{K_{eq}} * c_{P_1} * c_{P_2} + \frac{V_2 * K_{S_1}}{K_{iP_1}} * c_{S_1} * c_{P_1} + \frac{V_2}{K_{iP_2}} * c_{S_1} * c_{S_2} * c_{P_2} + \frac{V_1}{K_{iS_2} * K_{eq}} * c_{S_2} * c_{P_1} * c_{P_2}}$"^^La Te X ep
in defining formulation dp "$K_{P_1}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{P_2}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{S_1}$, Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{S_2}$, Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{eq}$, Equilibrium Constant"^^La Te X ep
in defining formulation dp "$K_{iP_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$K_{iP_2}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$K_{iS_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$K_{iS_2}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$V_1$, Reaction Rate"^^La Te X ep
in defining formulation dp "$V_2$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Reaction Rate"^^La Te X ep

Michaelis Menten Equation (Bi Bi Reaction Ordered without Products - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationforBiBiReactionOrderedMechanismwithoutProductsSS

Michaelis Menten Equation for Bi Bi Reaction with Ordered Mechanism and without Products following Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model without Products (Steady State Assumption) ni
contains quantity op Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Forward) ni
contains quantity op Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
defining formulation dp "$v_0 = \frac{V_{max,f} * c_{S_1} * c_{S_2}}{K_{iS_1} * K_{S_2} +K_{S_2} * c_{S_1} + K_{S_1} * c_{S_2} + c_{S_1} * c_{S_2}}$"^^La Te X ep
in defining formulation dp "$K_{S_1}$, Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{S_2}$, Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{iS_1}$, Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism - Forward)"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Michaelis Menten Equation (Bi Bi Reaction Ordered without Products and single central Complex - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationforBiBiReactionOrderedMechanismwithoutProductsSingleCCSS

Michaelis Menten Equation for Bi Bi Reaction with Ordered Mechanism without Products and single central Complex following Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model without Products and single central Complex (Steady State Assumption) ni
contains formulation op Inhibition Constant Substrate 1 (Bi Bi Reaction Ordered - Single central Complex - Michaelis Menten Model - Steady State Assumption) ni
contains quantity op Concentration ni
contains quantity op Inhibition Constant ni
contains quantity op Limiting Reaction Rate (Bi Bi Reaction Ordered Mechanism with single central Complex - Forward) ni
contains quantity op Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption) ni
contains quantity op Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption) ni
contains quantity op Reaction Rate ni
defining formulation dp "$v_0 = \frac{V_1 * c_{S_1} * c_{S_2}}{K_{iS_1} * K_{S_2} +K_{S_2} * c_{S_1} + K_{S_1} * c_{S_2} + c_{S_1} * c_{S_2}}$"^^La Te X ep
in defining formulation dp "$K_{S_1}$, Michaelis Constant Substrate 1 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{S_2}$, Michaelis Constant Substrate 2 (Bi Bi Reaction Ordered with single central Complex - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{iS_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$V_1$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Reaction Rate"^^La Te X ep

Michaelis Menten Equation (Bi Bi Reaction Ping Pong with Product 1 - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationBiBiReactionPingPongMechanismwithProduct1SS

belongs to
Mathematical Formulation c
has facts
contains formulation op Inhibition Constant Product 1 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Inhibition Constant Substrate 1 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Limiting Reaction Rate Forward (Bi Bi Reaction Ping Pong) ni
contains formulation op Michaelis Constant Substrate 1 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Substrate 2 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni
contains quantity op Concentration ni
contains quantity op Inhibition Constant ni
contains quantity op Michaelis Constant ni
contains quantity op Reaction Rate ni
generalized by formulation op Michaelis Menten Equation (Bi Bi Reaction Ping Pong with Products 1 and 2 - Michaelis Menten Model - Steady State Assumption) ni
defining formulation dp "$v_0 = \frac{V_{1} * c_{S_1} * c_{S_2}}{K_{S_2} * c_{S_1} + K_{S_1} * c_{S_2} + c_{S_1} * c_{S_2} + \frac{K_{iS_1} * K_{S_2}}{K_{iP_1}} * c_{P_1} + \frac{K_{S_2}}{K_{iP_1}} * c_{S_1} * c_{P_1}}$"^^La Te X ep
in defining formulation dp "$K_{S_1}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{S_2}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{iP_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$K_{iS_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$V_{1}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Reaction Rate"^^La Te X ep

Michaelis Menten Equation (Bi Bi Reaction Ping Pong with Product 2 - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationforBiBiReactionPingPongMechanismwithProduct2SS

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Bi Bi Reaction Ordered Mechanism Michaelis Menten Model with Product 2 and single central Complex (Steady State Assumption) ni
contains formulation op Inhibition Constant Product 2 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Inhibition Constant Substrate 2 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Limiting Reaction Rate Forward (Bi Bi Reaction Ping Pong) ni
contains formulation op Michaelis Constant Substrate 1 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Substrate 2 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni
contains quantity op Concentration ni
contains quantity op Inhibition Constant ni
contains quantity op Michaelis Constant ni
contains quantity op Reaction Rate ni
generalized by formulation op Michaelis Menten Equation (Bi Bi Reaction Ping Pong with Products 1 and 2 - Michaelis Menten Model - Steady State Assumption) ni
similar to formulation op Michaelis Menten Equation (Bi Bi Reaction Ping Pong with Product 1 - Michaelis Menten Model - Steady State Assumption) ni
defining formulation dp "$v_0 = \frac{V_{1} * c_{S_1} * c_{S_2}}{K_{S_2} * c_{S_1} + K_{S_1} * c_{S_2} + c_{S_1} * c_{S_2} + \frac{K_{S_1} * K_{iS_2}}{K_{iP_2}} * c_{P_2} + \frac{K_{S_1}}{K_{iP_2}} * c_{S_1} * c_{P_2}}$"^^La Te X ep
in defining formulation dp "$K_{S_1}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{S_2}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{iP_2}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$K_{iS_2}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$V_{1}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Reaction Rate"^^La Te X ep

Michaelis Menten Equation (Bi Bi Reaction Ping Pong with Products 1 and 2 - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationforBiBiReactionPingPongMechanismwithProducts1and2SS

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Bi Bi Reaction Ping Pong Mechanism Michaelis Menten Model with Products 1 and 2 (Steady State Assumption) ni
contains formulation op Equilibrium Constant (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Inhibition Constant Product 1 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Inhibition Constant Product 2 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Inhibition Constant Substrate 1 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Inhibition Constant Substrate 2 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Limiting Reaction Rate Backward (Bi Bi Reaction Ping Pong) ni
contains formulation op Limiting Reaction Rate Forward (Bi Bi Reaction Ping Pong) ni
contains formulation op Michaelis Constant Product 1 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Product 2 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Substrate 1 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Substrate 2 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni
contains quantity op Concentration ni
contains quantity op Equilibrium Constant ni
contains quantity op Inhibition Constant ni
contains quantity op Michaelis Constant ni
contains quantity op Reaction Rate ni
defining formulation dp "$v_{0} = \frac{V_{1} * V_{2} * (c_{S_1} * c_{S_2} - \frac{c_{P_1} * c_{P_2}}{K_{eq}})}{V_{2} * K_{S_2} * c_{S_1} + V_{2} * K_{S_1} * c_{S_2} + \frac{V_{1} * K_{P_2}}{K_{eq}} * c_{P_2} + \frac{V_{1} * K_{P_1}}{K_{eq}} * c_{P_2} + V_{2} * c_{S_1} * c_{S_2} + \frac{V_{1} * K_{P_2}}{K_{iS_1} * K_{eq}} * c_{S_1} * c_{P_1} +\frac{V_{1}}{K_{eq}} * c_{P_1} * c_{P_2} + \frac{V_{2} * K_{S_1}}{K_{iP_2}} * c_{S_2} * c_{P_2}}$"^^La Te X ep
in defining formulation dp "$K_{P_1}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{P_2}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{S_1}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{S_2}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{eq}$, Equilibrium Constant"^^La Te X ep
in defining formulation dp "$K_{iP_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$K_{iP_2}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$K_{iS_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$K_{iS_2}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$V_{1}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$V_{2}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Reaction Rate"^^La Te X ep

Michaelis Menten Equation (Bi Bi Reaction Ping Pong without Products - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationforBiBiReactionPingPongMechanismwithoutProductsSS

belongs to
Mathematical Formulation c
has facts
contains formulation op Limiting Reaction Rate Forward (Bi Bi Reaction Ping Pong) ni
contains formulation op Michaelis Constant Substrate 1 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Substrate 2 (Bi Bi Reaction Ping Pong - Michaelis Menten Model - Steady State Assumption) ni
contains quantity op Concentration ni
contains quantity op Michaelis Constant ni
contains quantity op Reaction Rate ni
generalized by formulation op Michaelis Menten Equation (Bi Bi Reaction Ping Pong with Product 1 - Michaelis Menten Model - Steady State Assumption) ni
generalized by formulation op Michaelis Menten Equation (Bi Bi Reaction Ping Pong with Product 2 - Michaelis Menten Model - Steady State Assumption) ni
generalized by formulation op Michaelis Menten Equation (Bi Bi Reaction Ping Pong with Products 1 and 2 - Michaelis Menten Model - Steady State Assumption) ni
defining formulation dp "${v_0}=\frac{V_{1}*c_{S_1}*c_{S_2}}{K_{S_2}*c_{S_1}+K_{S_1}*c_{S_2}+c_{S_1}*c_{S_2}}$"^^La Te X ep
in defining formulation dp "$K_{S_1}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{S_2}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$V_{1}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$v_{0}$, Reaction Rate"^^La Te X ep

Michaelis Menten Equation (Bi Bi Reaction Theorell-Chance with Product 1 - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationforBiBiReactionTheorellChanceMechanismwithProduct1SS

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Bi Bi Reaction Theorell-Chance Mechanism Michaelis Menten Model with Product 1 (Steady State Assumption) ni
contains formulation op Inhibition Constant Product 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Inhibition Constant Substrate 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Inhibition Constant Substrate 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Limiting Reaction Rate Backward (Bi Bi Reaction Theorell-Chance) ni
contains formulation op Limiting Reaction Rate Forward (Bi Bi Reaction Theorell-Chance) ni
contains formulation op Michaelis Constant Product 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Product 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Substrate 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Substrate 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains quantity op Concentration ni
contains quantity op Inhibition Constant ni
contains quantity op Michaelis Constant ni
contains quantity op Reaction Rate ni
defining formulation dp "$v_{0} = \frac{V_1 * c_{S_1} * c_{S_2}}{K_{iS_1} * K_{S_2} + K_{S_2} * c_{S_1} + K_{S_1} * c_{S_2} + c_{S_1} * c_{S_2} + \frac{K_{S_1} * K_{iS_2}}{K_{iP_1}} * c_{P_1} + \frac{K_{S_2}}{K_{iP_1}} * c_{S_1} * c_{P_1}}$"^^La Te X ep
in defining formulation dp "$K_{S_1}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{S_2}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{iP_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$K_{iS_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$K_{iS_2}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$V_{1}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Reaction Rate"^^La Te X ep

Michaelis Menten Equation (Bi Bi Reaction Theorell-Chance with Product 2 - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationforBiBiReactionTheorellChanceMechanismwithProduct2SS

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Bi Bi Reaction Theorell-Chance Mechanism Michaelis Menten Model with Product 2 (Steady State Assumption) ni
contains formulation op Inhibition Constant Product 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Inhibition Constant Substrate 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Limiting Reaction Rate Backward (Bi Bi Reaction Theorell-Chance) ni
contains formulation op Limiting Reaction Rate Forward (Bi Bi Reaction Theorell-Chance) ni
contains formulation op Michaelis Constant Product 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Product 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Substrate 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Substrate 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains quantity op Concentration ni
contains quantity op Inhibition Constant ni
contains quantity op Michaelis Constant ni
contains quantity op Reaction Rate ni
defining formulation dp "$v_{0} = \frac{V_1 * c_{S_1} * c_{S_2}}{K_{iS_1} * K_{S_2} + K_{S_2} * c_{S_1} + K_{S_1} * c_{S_2} + c_{S_1} * c_{S_2} + \frac{K_{iS_1} * K_{S_2}}{K_{iP_2}} * c_{P_2} + \frac{K_{S_1}}{K_{iP_2}} * c_{S_2} * c_{P_2}}$"^^La Te X ep
in defining formulation dp "$K_{S_1}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{S_2}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{iP_2}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$K_{iS_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$V_{1}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Reaction Rate"^^La Te X ep

Michaelis Menten Equation (Bi Bi Reaction Theorell-Chance with Products 1 and 2 - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationforBiBiReactionTheorellChanceMechanismwithProducts1and2SS

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Bi Bi Reaction Theorell-Chance Mechanism Michaelis Menten Model with Products 1 and 2 (Steady State Assumption) ni
contains formulation op Equilibrium Constant (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Inhibition Constant Product 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Inhibition Constant Substrate 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Limiting Reaction Rate Backward (Bi Bi Reaction Theorell-Chance) ni
contains formulation op Limiting Reaction Rate Forward (Bi Bi Reaction Theorell-Chance) ni
contains formulation op Michaelis Constant Product 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Product 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Substrate 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Substrate 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains quantity op Concentration ni
contains quantity op Equilibrium Constant ni
contains quantity op Inhibition Constant ni
contains quantity op Michaelis Constant ni
contains quantity op Reaction Rate ni
defining formulation dp "$v_{0} = \frac{V_{1} * V_{2} * (c_{S_1} * c_{S_2} - \frac{c_{P_1} * c_{P_2}}{K_{eq}})}{V_2 * K_{iS_1} * K_{S_2} + V_2 * K_{S_2} * c_{S_1} + V_2 * K_{S_1} * c_{S_2} + \frac{V_1 * K_{P_2}}{K_{eq}} * c_{P_1} + \frac{V_1 * K_{P_1}}{K_{eq}} * c_{P_2} + V_2 * c_{S_1} * c_{S_2} + \frac{V_1 * K_{P_2}}{K_{iS_1} * K_{eq}} * c_{S_1} * c_{P_1} + \frac{V_2 * K_{S_1}}{K_{iP_2}} * c_{S_2} * c_{P_2} + \frac{V_1}{K_{eq}} * c_{P_1} * c_{P_2}}$"^^La Te X ep
in defining formulation dp "$K_{P_1}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{P_2}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{S_1}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{S_2}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{eq}$, Equilibrium Constant"^^La Te X ep
in defining formulation dp "$K_{iP_2}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$K_{iS_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$V_{1}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$V_{2}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Reaction Rate"^^La Te X ep

Michaelis Menten Equation (Bi Bi Reaction Theorell-Chance without Products - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationforBiBiReactionTheorellChanceMechanismwithoutProductsSS

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Bi Bi Reaction Theorell-Chance Mechanism Michaelis Menten Model without Products (Steady State Assumption) ni
contains formulation op Inhibition Constant Product 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Inhibition Constant Substrate 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Limiting Reaction Rate Backward (Bi Bi Reaction Theorell-Chance) ni
contains formulation op Limiting Reaction Rate Forward (Bi Bi Reaction Theorell-Chance) ni
contains formulation op Michaelis Constant Product 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Product 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Substrate 1 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains formulation op Michaelis Constant Substrate 2 (Bi Bi Reaction Theorell-Chance - Michaelis Menten Model - Steady State Assumption) ni
contains quantity op Concentration ni
contains quantity op Inhibition Constant ni
contains quantity op Michaelis Constant ni
contains quantity op Reaction Rate ni
defining formulation dp "$v_{0} = \frac{V_1 * c_{S_1} * c_{S_2}}{K_{iS_1} * K_{S_2} + K_{S_2} * c_{S_1} + K_{S_1} * c_{S_2} + c_{S_1} * c_{S_2}}$"^^La Te X ep
in defining formulation dp "$K_{S_1}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{S_2}$, Michaelis Constant"^^La Te X ep
in defining formulation dp "$K_{iS_1}$, Inhibition Constant"^^La Te X ep
in defining formulation dp "$V_{1}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Reaction Rate"^^La Te X ep

Michaelis Menten Equation (Uni Uni Reaction with Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationforUniUniReactionwithProductSteadyStateAssumption

Michaelis Menten Equation for Uni Uni Reaction with Product following Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Backward) ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Product (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Product Concentration ni
contains quantity op Substrate Concentration ni
defining formulation dp "$v_{0}=\frac{\frac{V_{max,f}}{K_{S}}*c_{S}-\frac{V_{max,b}}{K_{P}}*c_{P}}{1+\frac{c_{S}}{K_{S}}+\frac{c_{P}}{K_{P}}}$"^^La Te X ep
in defining formulation dp "$K_{P}$, Michaelis Constant Product (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{S}$, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$V_{max,b}$, Limiting Reaction Rate (Uni Uni Reaction - Backward)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_P$, Product Concentration"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_{0}$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Michaelis Menten Equation (Uni Uni Reaction without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationforUniUniReactionwithoutProductSteadyStateAssumption

Michaelis Menten Equation for Uni Uni Reaction without Product following Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
defining formulation dp "$v_0 = \frac{V_{max,f} * c_{S}}{K_{S} + c_{S}}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Michaelis Menten Equation (Uni Uni Reaction without Product - Irreversibility Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationforUniUniReactionwithoutProductIrreversibilityAssumption

Michaelis Menten Equation for Uni Uni Reaction without Product following Irreversibility Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Irreversibility Assumption) ni
contains quantity op Substrate Concentration ni
defining formulation dp "$v_0 = \frac{V_{max,f} * c_{S}}{K_{S} + c_{S}}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Irreversibility Assumption)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Michaelis Menten Equation (Uni Uni Reaction without Product - Rapid Equilibrium Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationforUniUniReactionwithoutProductRapidEquilibriumAssumption

Michaelis Menten Equation for Uni Uni Reaction without Product following Rapid Equilibrium Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Rapid Equilibrium Assumption) ni
contains quantity op Substrate Concentration ni
defining formulation dp "$v_0 = \frac{V_{max,f} * c_{S}}{K_{S} + c_{S}}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Rapid Equilibrium Assumption)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Michaelis Menten Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationUniUniReactionwithoutProductandCompetitiveCompleteInhibitionSteadyStateAssumption

Michaelis Menten Equation for Uni Uni Reaction without Product and competitive complete Inhibition following Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
defining formulation dp "$v_0 = \frac{V_{max,f} * c_S}{c_S + K_S * (1 + \frac{c_I}{K_{ic}})}$"^^La Te X ep
in defining formulation dp "$K_S$,Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{ic}$,Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$,Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$,Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Michaelis Menten Equation (Uni Uni Reaction without Product and Competitive Partial Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationUniUniReactionwithoutProductandCompetitivePartialInhibitionSteadyStateAssumption

Michaelis Menten Equation for Uni Uni Reaction without Product and competitive partial Inhibition following Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
defining formulation dp "$v_0 = \frac{V_{max,f} * c_S}{K_S * \frac{(1+\frac{c_I}{K_{ic}})}{(1+\frac{c_I}{K_{iu}})} + C_S}$"^^La Te X ep
in defining formulation dp "$K_S$,Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{ic}$,Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$K_{iu}$,Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$,Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$,Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Michaelis Menten Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationUniUniReactionwithoutProductandMixedCompleteInhibitionSteadyStateAssumption

Michaelis Menten Equation for Uni Uni Reaction without Product and mixed complete Inhibition following Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
defining formulation dp "$v_0 = \frac{V_{max,f} * c_S}{K_S * (1 + \frac{c_I}{K_{ic}}) + (1 + \frac{c_I}{K_{iu}}) * c_S}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{ic}$, Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$K_{iu}$, Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$, Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Michaelis Menten Equation (Uni Uni Reaction without Product and Mixed Partial Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationUniUniReactionwithoutProductandMixedPartialInhibitionSteadyStateAssumption

Michaelis Menten Equation for Uni Uni Reaction without Product and mixed partial Inhibition following Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Limiting Reaction Rate with Inhibitor (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
defining formulation dp "$v_0 = \frac{(V_{max,f} + \frac{V_{max,I,f}*c_I}{K_{iu}}) * c_S}{K_S * (1 + \frac{c_I}{K_{ic}}) + (1 + \frac{c_I}{K_{iu}}) * c_S}$"^^La Te X ep
in defining formulation dp "$K_S$, Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{ic}$, Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$K_{iu}$, Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,I,f}$, Limiting Reaction Rate with Inhibitor (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$, Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$, Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Michaelis Menten Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationUniUniReactionwithoutProductandNonCompetitiveCompleteInhibitionSteadyStateAssumption

Michaelis Menten Equation for Uni Uni Reaction without Product and non-competitive complete Inhibition following Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
similar to formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni
defining formulation dp "$v_0 = \frac{V_{max,f} * c_S}{(1 + \frac{c_I}{K_{ic}}) * K_S + (1 + \frac{c_I}{K_{iu}}) * c_S}$"^^La Te X ep
in defining formulation dp "$K_S$,Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{ic}$,Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$K_{iu}$,Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$,Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$,Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Michaelis Menten Equation (Uni Uni Reaction without Product and Non-Competitive Partial Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationUniUniReactionwithoutProductandNonCompetitivePartialInhibitionSteadyStateAssumption

Michaelis Menten Equation for Uni Uni Reaction without Product and non-competitive partial Inhibition following Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Limiting Reaction Rate with Inhibitor (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
similar to formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Mixed Partial Inhibition - Steady State Assumption) ni
defining formulation dp "$v_0 = \frac{(V_{max,f} + \frac{V_{max,I,f}*c_I}{K_{iu}}) * c_S}{K_S * (1 + \frac{c_I}{K_{ic}}) + (1 + \frac{c_I}{K_{iu}}) * c_S}$"^^La Te X ep
in defining formulation dp "$K_S$,Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{ic}$,Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$K_{iu}$,Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,I,f}$, Limiting Reaction Rate with Inhibitor (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$,Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$,Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Michaelis Menten Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationUniUniReactionwithoutProductandUncompetitiveCompleteInhibitionSteadyStateAssumption

Michaelis Menten Equation for Uni Uni Reaction without Product and uncompetitive complete Inhibition following Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
defining formulation dp "$v_0 = \frac{V_{max,f} * c_S}{K_S + (1 + \frac{c_I}{K_{iu}}) *c_S}$"^^La Te X ep
in defining formulation dp "$K_S$,Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{iu}$,Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$,Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$,Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Michaelis Menten Equation (Uni Uni Reaction without Product and Uncompetitive Partial Inhibition - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MichaelisMentenEquationUniUniReactionwithoutProductandUncompetitivePartialInhibitionSteadyStateAssumption

Michaelis Menten Equation for Uni Uni Reaction without Product and uncompetitive partial Inhibition following Steady State Assumption
belongs to
Mathematical Formulation c
has facts
contains quantity op Inhibitor Concentration ni
contains quantity op Initial Reaction Rate ni
contains quantity op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains quantity op Limiting Reaction Rate with Inhibitor (Uni Uni Reaction - Forward) ni
contains quantity op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains quantity op Substrate Concentration ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
defining formulation dp "$v_0 = \frac{(V_{max,f} + \frac{V_{max,I,f}*c_I}{K_{iu}}) * c_S}{K_S + (1 + \frac{c_I}{K_{iu}}) * c_S}$"^^La Te X ep
in defining formulation dp "$K_S$,Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption)"^^La Te X ep
in defining formulation dp "$K_{iu}$,Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$V_{max,I,f}$, Limiting Reaction Rate with Inhibitor (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$V_{max,f}$, Limiting Reaction Rate (Uni Uni Reaction - Forward)"^^La Te X ep
in defining formulation dp "$c_I$,Inhibitor Concentration"^^La Te X ep
in defining formulation dp "$c_S$,Substrate Concentration"^^La Te X ep
in defining formulation dp "$v_0$, Initial Reaction Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Mixed Enzyme Inhibition Coupling Condition (Uni Uni Reaction)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MixedEnzymeInhibitionCouplingConditionUniUniReaction

coupling condition for a mixed enzyme inhibition in an uni uni reaction
belongs to
Mathematical Formulation c
has facts
defining formulation dp "$K_{ic} \neq K_{iu}$"^^La Te X ep
in defining formulation dp "$K_{ic}$,Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$K_{iu}$,Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean

Mobility Of Electronsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MobilityOfElectrons

For use in semiconductor physics
belongs to
Quantity c
has facts
description ap "magnitude of the drift velocity of electrons per unit electric field"@en

Mobility Of Holesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MobilityOfHoles

For use in semiconductor physics
belongs to
Quantity c
has facts
description ap "measure of how easily holes can move through the material under the influence of an electric field"@en

Model Order Reductionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ModelOrderReduction

After spatial discretization of PDEa, solving the resulting large-scale systems of ODEs can therefore become incredibly time-consuming. Developed from well established mathematical theory and robust numerical algorithms, Model Order Reduction (MOR) has been recognized as very efficient for reducing the simulation time of large-scale systems
belongs to
Computational Task c
has facts
generalizes task op Balanced Truncation ni
generalizes task op H2 Optimal Approximation ni
description ap "technique in mathematical modeling to effectively reduce the dimensionality of a model"@en
doi I D ap 978 1 4471 5102 9 142 1 ep
wikidata I D ap Q12202921 ep

Molecular Alignmentni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MolecularAlignment

Typically achieved by the interaction of induced dipole moments with external laser fields
belongs to
Mathematical Formulation c
has facts
contains quantity op Polar Angle ni
contains quantity op Quantum State Vector ni
defining formulation dp "$A = \langle \psi | \cos^2 \theta | \psi \rangle$"^^La Te X ep
in defining formulation dp "$\psi$, Quantum State Vector"^^La Te X ep
in defining formulation dp "$\theta$, Polar Angle"^^La Te X ep
description ap "expectation value indicating in how far molecular axes are parallel to space fxed axes"@en

Molecular Dynamicsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Molecular_Dynamics

belongs to
Research Problem c
has facts
contained in field op Physical Chemistry ni
generalizes problem op Molecular Reaction Dynamics ni
modeled by op Classical Dynamics Model ni
modeled by op Classical Langevin Model ni
modeled by op Quantum Classical Model ni
modeled by op Quantum Model (Closed System) ni
modeled by op Quantum Model (Open System) ni
description ap "physical movements of atoms and molecules in a gas, a liquid, a solid, etc"@en
wikidata I D ap MathModDB Ontology ep

Molecular Orientationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MolecularOrientation

Typically achieved by the interaction of permanent dipole moments with external electrostatic fields.
belongs to
Mathematical Formulation c
has facts
contains quantity op Polar Angle ni
contains quantity op Quantum State Vector ni
defining formulation dp "$O = \langle \psi | \cos \theta | \psi \rangle$"^^La Te X ep
in defining formulation dp "$\psi$, Quantum State Vector"^^La Te X ep
in defining formulation dp "$\theta$, Polar Angle"^^La Te X ep
description ap "expectation value indicating in how far molecular axes point in the same direction as space fxed axes"@en

Molecular Physicsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MolecularPhysics

belongs to
Research Field c
has facts
contains problem op Molecular Reaction Dynamics ni
contains problem op Molecular Rotation ni
contains problem op Molecular Spectroscopy ni
contains problem op Molecular Spectroscopy (Transient) ni
contains problem op Molecular Spectrosopy (Stationary) ni
contains problem op Molecular Vibration ni
contains problem op Molecular Dynamics ni
description ap "study of the physical properties of molecules.Significant overlaps with physical chemistry, chemical physics, and quantum chemistry"@en
wikidata I D ap Q489328 ep

Molecular Reaction Dynamicsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MolecularReactionDynamics

Although there were first attempts in the 1930s (first trajectory calculations for H+H2 reaction calculated by Polanyi in Berlin-Dahlem), this field has strongy evolved since the 1970s and 1980s with the upcoming of short laser pulses.
belongs to
Research Problem c
has facts
contained in field op Physical Chemistry ni
modeled by op Classical Dynamics Model ni
modeled by op Quantum Classical Model ni
modeled by op Quantum Model (Closed System) ni
description ap "branch of physical chemistry that deals with observing and understang chemical reactions in real time and on an atomistic basis"@en

Molecular Rotationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MolecularRotation

belongs to
Research Problem c
has facts
generalized by problem op Molecular Spectroscopy ni
modeled by op Linear Rotor (Apolar) ni
modeled by op Linear Rotor (Combined) ni
modeled by op Linear Rotor (Non-Rigid) ni
modeled by op Linear Rotor (Polar) ni
description ap "rotation of a molecule about its center of mass. Often, molecules are assumed to rotate like rigid bodies, but there can also be centrifugal distortion"@en
wikidata I D ap Q1234926 ep
wikidata I D ap Q904380 ep

Molecular Spectroscopyni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MolecularSpectroscopy

Rotations are collective motions of the atomic nuclei and typically lead to spectra in the microwave and millimeter-wave spectral regions. Vibrations are relative motions of the atomic nuclei and are studied by both infrared and Raman spectroscopy. Electronic excitations are studied using visible and ultraviolet spectroscopy as well as fluorescence spectroscopy
belongs to
Research Problem c
has facts
contained in field op Physical Chemistry ni
generalizes problem op Molecular Spectroscopy (Transient) ni
generalizes problem op Molecular Spectrosopy (Stationary) ni
description ap "measurement (or simulation) of interactions between electromagnetic waves and matter"@en
wikidata I D ap Q1943412 ep

Molecular Spectroscopy (Transient)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MolecularSpectroscopyTransient

This discipline evolved since the 1980s, with the upcoming of pico-second, femto-second and eventually even atto-second laser pulses.
belongs to
Research Problem c
has facts
contained in field op Physical Chemistry ni
modeled by op Classical Dynamics Model ni
modeled by op Quantum Classical Model ni
modeled by op Quantum Model (Closed System) ni
description ap "observing molecular dynamics by spectroscopy in real time"@en

Molecular Spectrosopy (Stationary)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MolecularSpectrosopyStationary

For example, molecular vibrational states can be detected by infrared or Raman spectroscopy
belongs to
Research Problem c
has facts
contained in field op Physical Chemistry ni
modeled by op Classical Dynamics Model ni
modeled by op Quantum Classical Model ni
modeled by op Quantum Model (Closed System) ni
modeled by op Quantum Model (Open System) ni
description ap "studying molecular energy levels by stationary, i.e. time-independent molecular spectrosopy"@en

Molecular Vibrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MolecularVibration

Often modeled within the harmonic approximation, but there can be also effects of anharmonicity
belongs to
Research Problem c
has facts
generalized by problem op Molecular Spectroscopy ni
modeled by op Normal Modes ni
modeled by op Normal Modes (Anharmonic) ni
modeled by op Normal Modes (Harmonic) ni
modeled by op Normal Modes (Intermolecular) ni
description ap "periodic motion of the atoms of a molecule around their equilibrium positions"@en
wikidata I D ap Q900121 ep

Molecularityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Molecularity

belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
description ap "number of reactant molecular entities that are involved in the 'microscopic chemical event' constituting an elementary reaction"@en
wikidata I D ap Q776329 ep

Momentumni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Momentum

conserved physical quantity related to the motion of a body
belongs to
Quantity Kind c
has facts
qudt I D ap Momentum ep
wikidata I D ap Q41273 ep

Momentum Balance Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MomentumBalanceEquation

These equations are known as the momentum balance equations because the momentum fluxes are balanced by body and surface forces.
belongs to
Mathematical Formulation c
has facts
contains quantity op Eigenstress Of Crystal ni
contains quantity op Stress Of Crystal ni
defining formulation dp "$\nabla\cdot(\sigma-\sigma^\ast)=0$"^^La Te X ep
in defining formulation dp "$\sigma$, Stress Of Crystal"^^La Te X ep
in defining formulation dp "$\sigma^\ast$, Eigenstress Of Crystal"^^La Te X ep
description ap "in the theory of elasticity, the conservation of momentum can also be written in vector form"@en

Monodomain Equation for Action Potential Propagationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Monodomain_Equation_for_Action_Propagation_Potential

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Action Potential Propagation Model ni
contains quantity op Effective Conductivity ni
contains quantity op Ion Current ni
contains quantity op Membrane Capacitance ni
contains quantity op Time ni
contains quantity op Transmembrane Potential ni
defining formulation dp "$$\frac{\partial V^\text{f}_\text{m}}{\partial t} = \frac{1}{C^\text{f}_\text{m}} \left( \frac{1}{A_\text{m}} \sigma_{\text{eff}} \frac{\partial^2 V^{\text{f}}_{\text{m}}}{\partial s^2} - I_\text{ion} (V^{\text{f}}_{\text{m}}, \mathbf{y}) + S(V^{\text{s}}_{\text{m}})\right)~ \text{in $\Omega_{f}$}$$"^^La Te X ep
in defining formulation dp "$C^{\text{f}}_{\text{m}}$, Membrane Capacitance"^^La Te X ep
in defining formulation dp "$I_{\text{ion}}$, Ion Current"^^La Te X ep
in defining formulation dp "$V^{\text{f}}_{\text{m}}$, Transmembrane Potential"^^La Te X ep
in defining formulation dp "$\sigma_{\text{eff}}$, Effective Conductivity"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
description ap "describes the evelution of the transmembrane potential at each sacomeres location i.e. the propagation of the action potential"@en
description ap "the evelution of the transmembrane potential at each sacomeres location"@en

MOR Transformation Matrixni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MOR_TransformationMatrix

belongs to
Quantity c
has facts
description ap "transformation matrix, to be applied to the input-output formulation of linear or bilinear control systems"@en

Mortality Modelingni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MortalityModeling

belongs to
Research Problem c
has facts
modeled by op Gamma-Gompertz-Makeham Model ni
description ap "science of determining likely future mortality rates"@en

Motor Neuron Pool Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Motor_Neuron_Pool_Model

belongs to
Mathematical Model c
has facts
studied in op Homs-Pons (2024) Coupled simulations and parameter inversion for neural system and electrophysiological muscle models ni
is deterministic dp "true"^^boolean
is dynamic dp "true"^^boolean
is time-continuous dp "true"^^boolean
description ap "mathematical model of neuromuscular system based on the agonist-antagonist myoneural interface"@en
doi I D ap gamm.202370009 ep

Motor Neuron Pool ODE Systemni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Motor_Neuron_Pool_ODE_System

Two coupled ODEs which describe the membrane potentials in the soma and the dendrite compartments.
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Motor Neuron Pool Model ni
contains quantity op Coupling Current ni
contains quantity op Fiber Contraction Velocity ni
contains quantity op Fiber Stretch ni
contains quantity op Ion Current ni
contains quantity op Membrane Capacitance ni
contains quantity op Membrane Potential ni
contains quantity op Neural Input ni
contains quantity op Sensory Organ Current ni
contains quantity op Time ni
defining formulation dp "$$\begin{align*} \frac{\text{d}V^{\text{d}}_{\text{m}}}{\text{d}t} &= \frac{1}{C^{\text{d}}_{\text{m}}}\left(-I^{\text{d}}_{\text{ion}}(V^{\text{d}}_{\text{m}}) - I^{\text{d}}_{\text{C}}(V^{\text{d}}_{\text{m}},V^{\text{s}}_{\text{m}}) \right) \\ \frac{\text{d}V^{\text{s}}_{\text{m}}}{\text{d}t} &= \frac{1}{C^{\text{s}}_{\text{m}}}\left(-I^{\text{s}}_{\text{ion}}(V^{\text{s}}_{\text{m}}) - I^{\text{s}}_{\text{C}}(V^{\text{d}}_{\text{m}},V^{\text{s}}_{\text{m}}) + I_{\text{spindle}}(\lambda_{\text{f}}, \dot{\lambda}_\text{f}) + I_\text{ext} \right) \\ \end{align*}$$"^^La Te X ep
in defining formulation dp "$t$, Time"
in defining formulation dp "$C_{\text{m}}$, Membrane Capacitance"^^La Te X ep
in defining formulation dp "$I_{\text{C}}$, Coupling Current"^^La Te X ep
in defining formulation dp "$I_{\text{ext}}$, Neural Input"^^La Te X ep
in defining formulation dp "$I_{\text{ion}}$, Ion Current"^^La Te X ep
in defining formulation dp "$I_{\text{spindle}}$, Sensory Organ Current"^^La Te X ep
in defining formulation dp "$V_{\text{m}}$, Membrane Potential"^^La Te X ep
in defining formulation dp "$\lambda_{\text{f}}$, Fibre Contraction Velocity"^^La Te X ep
in defining formulation dp "$\lambda_{\text{f}}$, Fibre Stretch"^^La Te X ep
description ap "two coupled ODEs which describe the membrane potentials"@en

Multi-Population Discrete Susceptible Infectious Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MultiPopulationSusceptibleInfectiousModel

belongs to
Mathematical Model c
has facts
generalizes op Discrete Susceptible Infectious Model ni
models op Spreading of Infectious Diseases ni
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean
description ap "discrete-time multi-population susceptible infectious model"@en

Multi-Population Discrete Susceptible Infectious Removed Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MultiPopulationSusceptibleInfectiousRemovedModel

belongs to
Mathematical Model c
has facts
generalizes op Discrete Susceptible Infectious Removed Model ni
models op Spreading of Infectious Diseases ni
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean
description ap "discrete-time multi-population susceptible infectious removed model"@en

Multi-Population Discrete Susceptible Infectious Susceptible Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MultiPopulationSusceptibleInfectiousSusceptibleModel

belongs to
Mathematical Model c
has facts
generalizes op Discrete Susceptible Infectious Susceptible Model ni
models op Spreading of Infectious Diseases ni
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean
description ap "discrete-time multi-population susceptible infectious susceptible model"@en

Multipolar Expansion Model (3D)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MultipolarExpansionModel3D

Multipole expansions are often used to represent electromagnetic fields, where the fields at distant points are given in terms of sources (charges and/or currents) in a small region (far field limit). The first term is called the monopole moment, the second term is called the dipole moment, the third term the quadrupole moment, etc.
belongs to
Mathematical Model c
has facts
applied by task op Far Field Radiation ni
contains formulation op Spherical Harmonics Expansion (3D) ni
generalized by model op Maxwell Equations Model ni
models op Electromagnetic Fields And Waves ni
description ap "mathematical series approximating an angle-dependent function"@en
wikidata I D ap Q1027847 ep

Muscle Contraction Velocityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MuscleContractionVelocity

belongs to
Quantity c
has facts
generalized by quantity op Velocity ni
description ap "muscle contraction velocity"@en

Muscle Lengthni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MuscleLength

belongs to
Quantity c
has facts
generalized by quantity op Length ni
description ap "length of a muscle"@en

Muscle Movementni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Muscle_Movement

belongs to
Research Problem c
has facts
description ap "process in which force is generated within muscle tissue, resulting in a change in muscle geometry"@en
wikidata I D ap "https://www.wikidata.org/wiki/Q127006"@en

Muscle Spindle Firing Rateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#MuscleSpindleFiringRate

belongs to
Quantity c
has facts
generalized by quantity op Neural Firing Rate ni
description ap "frequency at which sensory neurons within the muscle spindle transmit signals to the central nervous system"@en

Near Field Radiationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NearFieldRadiation

The near fieldis a region of the electromagnetic (EM) field around an object, such as a transmitting antenna, or the result of radiation scattering off an object. Non-radiative near-field behaviors dominate close to the antenna or scatterer.
belongs to
Computational Task c
has facts
applies model op Maxwell Equations Model ni
description ap "electromagnetic radiation behaviors that predominate at shorter distances"@en
wikidata I D ap Q6984336 ep

Neumann Boundary Conditionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NeumannBoundaryCondition

belongs to
Mathematical Formulation c
has facts
description ap "boundary condition specifying the values of derivatives of a solution of a differential equation along the boundaries of a domain"@en
alt Label ap "second-type boundary condition"@en
wikidata I D ap Q1149279 ep

Neumann Boundary Condition (Stress-Free Relaxation)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NeumannBoundaryConditionStressFreeRelaxation

belongs to
Mathematical Formulation c
has facts
contains quantity op Eigenstress Of Crystal ni
contains quantity op Stress Of Crystal ni
contains quantity op Unit Normal Vector ni
generalized by formulation op Neumann Boundary Condition ni
defining formulation dp "$(\sigma-\sigma^\ast)\cdot n=0$"^^La Te X ep
in defining formulation dp "$\sigma$, Stress Of Crystal"^^La Te X ep
in defining formulation dp "$\sigma^\ast$, Eigenstress Of Crystal"^^La Te X ep
in defining formulation dp "$n$, Normal Unit Vector"^^La Te X ep
description ap "Neumann boundary condition in theory of elasticity (stress-free relaxation)"@en

Neumann Boundary Condition For Electric Potentialni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NeumannBoundaryConditionElectricPotential

belongs to
Mathematical Formulation c
has facts
contains quantity op Electric Potential ni
contains quantity op Electrode Interfaces ni
contains quantity op Time ni
contains quantity op Unit Normal Vector ni
generalized by formulation op Neumann Boundary Condition ni
defining formulation dp "$n \cdot \nabla \psi(r,t)|_{\Gamma_N}=0$"^^La Te X ep
in defining formulation dp "$\Gamma_N$, Electrode Interfaces"^^La Te X ep
in defining formulation dp "$\psi$, Electric Potential"^^La Te X ep
in defining formulation dp "$n$, Normal Unit Vector"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
description ap "Typically used to indicate that the electric field should be perpendicalar to an electrode interface"@en

Neumann Boundary Condition For Electron Fermi Potentialni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NeumannBoundaryConditionForElectronFermiPotential

belongs to
Mathematical Formulation c
has facts
contained as boundary condition in op Drift-Diffusion Model ni
contains quantity op Electrode Interfaces ni
contains quantity op Fermi Potential For Electrons ni
contains quantity op Unit Normal Vector ni
generalized by formulation op Neumann Boundary Condition ni
defining formulation dp "$n \cdot \nabla \psi|_{\Gamma_N}=0$"^^La Te X ep
in defining formulation dp "$\Gamma_N$, Electrode Interfaces"^^La Te X ep
in defining formulation dp "$\phi_n$, Fermi Potential For Electrons"^^La Te X ep
in defining formulation dp "$n$, Normal Unit Vector"^^La Te X ep
description ap "Neumann boundary condition for the Fermi potential governing the electrons"@en

Neumann Boundary Condition For Hole Fermi Potentialni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NeumannBoundaryConditionForHoleFermiPotential

belongs to
Mathematical Formulation c
has facts
contained as boundary condition in op Drift-Diffusion Model ni
contains quantity op Electrode Interfaces ni
contains quantity op Fermi Potential For Holes ni
contains quantity op Unit Normal Vector ni
generalized by formulation op Neumann Boundary Condition ni
defining formulation dp "$n \cdot \nabla \phi_p|_{\Gamma_N}=0$"^^La Te X ep
in defining formulation dp "$\Gamma_N$, Electrode Interfaces"^^La Te X ep
in defining formulation dp "$\phi_p$, Fermi Potential For Holes"^^La Te X ep
in defining formulation dp "$n$, Normal Unit Vector"^^La Te X ep
description ap "Neumann boundary condition for the Fermi potential governing the holes"@en

Neumann Boundary Condition For SEIR Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NeumannBoundaryConditionForSEIRModel

Homogeneous Boundary Condition For the Full-PDe SEIR Model ensure that all the fractions of the population densities of susceptibles, exposed, infectious and removed add up to 1 at all times
belongs to
Mathematical Formulation c
has facts
contained as boundary condition in op PDE SEIR Model ni
contains quantity op Fraction Of Population Density Of Exposed ni
contains quantity op Fraction Of Population Density Of Infectious ni
contains quantity op Fraction Of Population Density Of Removed ni
contains quantity op Fraction Of Population Density Of Susceptibles ni
generalized by op Neumann Boundary Condition ni
defining formulation dp "$s + e + i + r = 1$"^^La Te X ep
in defining formulation dp "$e$, Fraction Of Population Density Of Exposed"^^La Te X ep
in defining formulation dp "$i$, Fraction Of Population Density Of Infectious"^^La Te X ep
in defining formulation dp "$r$, Fraction Of Population Density Of Removed"^^La Te X ep
in defining formulation dp "$s$, Fraction Of Population Density Of Susceptibles"^^La Te X ep

Neural Firing Rateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NeuralFiringRate

belongs to
Quantity c
has facts
generalized by quantity op Frequency ni
description ap "average number of electrical impulses, or spikes, a neuron generates per unit of time"@en
wikidata I D ap Q71762818 ep

Neural Inputni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NeuralInput

belongs to
Quantity c
has facts
generalized by quantity op Electric Current ni
description ap "neural input in a motor neuron pool model"@en

Noise Strengthni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NoiseStrength

noise caused by influences, uncertainties in the communication between individuals or free will
belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
description ap "noise modelling unknown external influences"@en

Non-Competitive Enzyme Inhibition Coupling Condition (Uni Uni Reaction)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NoncompetitiveEnzymeInhibitionCouplingConditionUniUniReaction

belongs to
Mathematical Formulation c
has facts
defining formulation dp "$$\begin{align*} k_{1} &= k_{5} \\ k_{-1} &= k_{-5} \\ k_{-3} &= k_{-4}\\ k_{3} &= k_{4} \\ K_{ic} &= K_{iu}\\ \end{align}$$"^^La Te X ep
in defining formulation dp "$K_{ic}$,Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$K_{iu}$,Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$k_1$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_3$,Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_4$,Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_5$,Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-1}$,Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-3}$,Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-4}$,Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-5}$,Reaction Rate Constant"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean
description ap "coupling condition for a non-competitive enzyme inhibition in an uni uni reaction"@en

Non-Local Meansni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NonLocalMeans

belongs to
Mathematical Formulation c
has facts
defining formulation dp "$u(p) = {1 \over C(p)}\int_\Omega v(q) f(p,q)dq$"^^La Te X ep
in defining formulation dp "$C(p)$, a normalizing factor"^^La Te X ep
in defining formulation dp "$\Omega$, the area of an image"^^La Te X ep
in defining formulation dp "$f(p,q)$, the weighting function"^^La Te X ep
in defining formulation dp "$u(p)$, filtered value of the iamge at point $p$"^^La Te X ep
in defining formulation dp "$v(q)$, the unfiltered value of the image at point $q$"^^La Te X ep
description ap "algorithm in image processing for image denoising"@en
doi I D ap C V P R.2005.38 ep
wikidata I D ap Q7048948 ep

Nonlinear Parameter Estimation (Uni Uni Reaction without Product - Michaelis Menten Model - Irreversibility Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NonlinearParameterEstimationUniUniReactionWithoutProductMMIrreversibility

nonlinear fit to determine the limiting reaction rate and michaelis constant
belongs to
Computational Task c
has facts
contains formulation op Michaelis Menten Equation (Uni Uni Reaction without Product - Irreversibility Assumption) ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Irreversibility Assumption) ni
generalized by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
is linear dp "false"^^boolean

Nonlinear Parameter Estimation (Uni Uni Reaction without Product - Michaelis Menten Model - Rapid Equilibrium Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NonlinearParameterEstimationUniUniReactionWithoutProductMMRapidEquilibrium

nonlinear fit to determine the limiting reaction rate and michaelis constant
belongs to
Computational Task c
has facts
contains formulation op Michaelis Menten Equation (Uni Uni Reaction without Product - Rapid Equilibrium Assumption) ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Rapid Equilibrium Assumption) ni
generalized by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
is linear dp "false"^^boolean

Nonlinear Parameter Estimation (Uni Uni Reaction without Product - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NonlinearParameterEstimationUniUniReactionWithoutProductMMSteadyState

nonlinear fit to determine the limiting reaction rate and michaelis constant
belongs to
Computational Task c
has facts
contains formulation op Michaelis Menten Equation (Uni Uni Reaction without Product - Steady State Assumption) ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
generalized by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
is linear dp "false"^^boolean

Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NonlinearParameterEstimationUniUniReactionwithoutProductandCompetitiveCompleteInhibitionMichaelisMentenModelSteadyStateAssumption

nonlinear fit to determine the limiting reaction rate, michaelis constant and inhibition constant
belongs to
Computational Task c
has facts
contains formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption) ni
contains input op Inhibitor Concentration ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
generalized by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
is linear dp "false"^^boolean

Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Competitive Partial Inhibition - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NonlinearParameterEstimationUniUniReactionwithoutProductandCompetitivePartialInhibitionMichaelisMentenModelSteadyStateAssumption

nonlinear fit to determine the limiting reaction rate, michaelis constant and inhibition constant
belongs to
Computational Task c
has facts
contains formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Competitive Partial Inhibition - Steady State Assumption) ni
contains input op Inhibitor Concentration ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains output op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
generalized by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
is linear dp "false"^^boolean

Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NonlinearParameterEstimationUniUniReactionwithoutProductandMixedCompleteInhibitionMichaelisMentenModelSteadyStateAssumption

nonlinear fit to determine the limiting reaction rate, michaelis constant and inhibition constants
belongs to
Computational Task c
has facts
contains formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni
contains input op Inhibitor Concentration ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains output op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
generalized by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
is linear dp "false"^^boolean

Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Mixed Partial Inhibition - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NonlinearParameterEstimationUniUniReactionwithoutProductandMixedPartialInhibitionMichaelisMentenModelSteadyStateAssumption

nonlinear fit to determine the limiting reaction rate, michaelis constant and inhibition constants
belongs to
Computational Task c
has facts
contains formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Mixed Partial Inhibition - Steady State Assumption) ni
contains input op Inhibitor Concentration ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Limiting Reaction Rate with Inhibitor (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains output op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
generalized by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
is linear dp "false"^^boolean

Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NonlinearParameterEstimationUniUniReactionwithoutProductandNonCompetitiveCompleteInhibitionMichaelisMentenModelSteadyStateAssumption

nonlinear fit to determine the limiting reaction rate, michaelis constant and inhibition constants
belongs to
Computational Task c
has facts
contains formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption) ni
contains input op Inhibitor Concentration ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains output op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
generalized by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
is linear dp "false"^^boolean

Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Non-Competitive Partial Inhibition - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NonlinearParameterEstimationUniUniReactionwithoutProductandNonCompetitivePartialInhibitionMichaelisMentenModelSteadyStateAssumption

nonlinear fit to determine the limiting reaction rate, michaelis constant and inhibition constants
belongs to
Computational Task c
has facts
contains formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Non-Competitive Partial Inhibition - Steady State Assumption) ni
contains input op Inhibitor Concentration ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Competitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Limiting Reaction Rate with Inhibitor (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains output op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
generalized by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
is linear dp "false"^^boolean

Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NonlinearParameterEstimationUniUniReactionwithoutProductandUncompetitiveCompleteInhibitionMichaelisMentenModelSteadyStateAssumption

nonlinear fit to determine the limiting reaction rate, michaelis constant and inhibition constant
belongs to
Computational Task c
has facts
contains formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption) ni
contains input op Inhibitor Concentration ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains output op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
generalized by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
is linear dp "false"^^boolean

Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Partial Inhibition - Michaelis Menten Model - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NonlinearParameterEstimationUniUniReactionwithoutProductandUncompetitivePartialInhibitionMichaelisMentenModelSteadyStateAssumption

nonlinear fit to determine the limiting reaction rate, michaelis constant and inhibition constant
belongs to
Computational Task c
has facts
contains formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Uncompetitive Partial Inhibition - Steady State Assumption) ni
contains input op Inhibitor Concentration ni
contains input op Initial Reaction Rate ni
contains input op Substrate Concentration ni
contains output op Limiting Reaction Rate (Uni Uni Reaction - Forward) ni
contains output op Limiting Reaction Rate with Inhibitor (Uni Uni Reaction - Forward) ni
contains output op Michaelis Constant Substrate (Uni Uni Reaction - Steady State Assumption) ni
contains output op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
generalized by task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
is linear dp "false"^^boolean

Nonlinear Parameter Estimation of Enzyme Kineticsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ParameterEstimationOfEnzymeKineticsNonlinear

Nonlinear Determination of the Kinetic Constants for Enzyme-catalyzed Reactions.
belongs to
Computational Task c
has facts
is linear dp "false"^^boolean
doi I D ap B978 0 12 801238 3.05143 6 ep

Nonrelativistic Approximationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NonrelativisticApproximation

belongs to
Mathematical Formulation c
has facts
contained as assumption in op Classical Dynamics Model ni
contained as assumption in op Classical Hamilton Equations ni
contained as assumption in op Classical Newton Equation ni
contains quantity op Classical Momentum ni
contains quantity op Relativistic Momentum ni
defining formulation dp "p_{rel} \approx p_{cl}"^^La Te X ep
in defining formulation dp "$p_{cl}$, Classical Momentum"^^La Te X ep
in defining formulation dp "$p_{rel}$, Relativistic Momentum"^^La Te X ep
description ap "Newtonian dynamics as an approximation to special relativity"@en

Normal Interaction Force Of Two Particlesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Normal_Interaction_Force_Of_Two_Particles

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Linear Discrete Element Method ni
contains quantity op Young Modulus ni
defining formulation dp "$\bm F^N_{ij}=\left(k_{ij}^N\delta_{ij}+d_{ij}^N\dot{\delta}_{ij}\right)\bm n_{ij}$ $\delta_{ij}=\langle \bm x_i - \bm x_j, \bm n_{ij}\rangle$ $\delta_{ij}=\langle \bm v_i - \bm v_j, \bm n_{ij}\rangle$ $\bm n_{ij} = \frac{\bm x_i - \bm x_j}{\lVert \bm x_i - \bm x_j \rVert}$ $k^N_{ij}=E_N \pi r_{ij} / 2$ $d_{ij}^N=D_N 2 \sqrt{k^N_{ij}m_{ij}}$ $m_{ij}=\frac{m_im_j}{m_i + m_j}$"^^La Te X ep
in defining formulation dp "$D_N$, control parameter of critical damping"^^La Te X ep
in defining formulation dp "$E_N$, Young Modulus"^^La Te X ep
in defining formulation dp "$\bm F^N_{ij}$, total normal force between particles $i$ and $j$"^^La Te X ep
in defining formulation dp "$\bm v_i\in \mathbb R^3$, velocity of particle $i$ $\bm v_j\in \mathbb R^3$, velocity of particle $j$"^^La Te X ep
in defining formulation dp "$\bm x_i\in \mathbb R^3$, position of center of gravity for particle $i$ $\bm x_j\in \mathbb R^3$, position of center of gravity for particle $j$"^^La Te X ep
in defining formulation dp "$r_{ij}=(r_i+r_j)/2$, mean radius of particles $i$ and $j$"^^La Te X ep
description ap "Component of the total force in normal direction, i.e. the sum of dissipative and conservative forces"@en

Normal Mode Coordinateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NormalModeCoordinate

Normal coordinates refer to the positions of atoms away from their equilibrium positions, wrt a normal mode of vibration. Formally, normal modes are determined by solving a secular determinant, and then the normal coordinates can be expressed as a summation over the cartesian coordinates (over the atom positions). The normal modes diagonalize the matrix governing the molecular vibrations.
belongs to
Quantity c
has facts
description ap "pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation"@en
wikidata I D ap Q112730947 ep

Normal Mode Coordinate (Dimensionless)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NormalModeCoordinateDimensionless

belongs to
Quantity c
has facts
defined by op Normal Mode Coordinate (Dimensionless, Definition) ni
nondimensionalizes quantity op Normal Mode Coordinate ni
description ap "nondimensionalized positions of atoms away from their equilibrium positions, wrt a normal mode of vibration"@en

Normal Mode Coordinate (Dimensionless, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NormalModeCoordinateDefinition

belongs to
Mathematical Formulation c
has facts
contains quantity op Normal Mode Coordinate ni
contains quantity op Normal Mode Coordinate (Dimensionless) ni
contains quantity op Planck Constant ni
contains quantity op Speed Of Light ni
contains quantity op Vibration Frequency (Harmonic) ni
defining formulation dp "$\begin{align} q&=&\sqrt{\gamma}Q \\ \gamma&=&\frac{2 \pi c \omega}{\hbar} \end{align}$"^^La Te X ep
in defining formulation dp "$Q$, Normal Mode Coordinate"^^La Te X ep
in defining formulation dp "$\hbar$, Planck Constant"^^La Te X ep
in defining formulation dp "$\omega$, Vibration Frequency (Harmonic)"^^La Te X ep
in defining formulation dp "$c$, Speed of Light"^^La Te X ep
in defining formulation dp "$q$, Normal Mode Coordinate (Dimensionless)"^^La Te X ep
description ap "nondimensionalized positions of atoms away from their equilibrium positions, wrt a normal mode of vibration"@en

Normal Mode Momentumni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NormalModeMomentum

belongs to
Quantity c
has facts
description ap "canonical momenta, corresponding to the normal mode coordinates used for the description of vibrations of many-body systems, e.g. molecules"@en
wikidata I D ap Q112730947 ep

Normal Mode Momentum (Dimensionless)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NormalModeMomentumDimensionless

belongs to
Quantity c
has facts
defined by op Normal Mode Momentum (Dimensionless, Definition) ni
nondimensionalizes quantity op Normal Mode Momentum ni
description ap "dimensionless canonical momenta, corresponding to the normal mode coordinates used for the description of vibrations of many-body systems, e.g. molecules"@en

Normal Mode Momentum (Dimensionless, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NormalModeMomentumDefinition

belongs to
Mathematical Formulation c
has facts
contains quantity op Normal Mode Momentum ni
contains quantity op Normal Mode Momentum (Dimensionless) ni
contains quantity op Planck Constant ni
contains quantity op Speed Of Light ni
contains quantity op Vibration Frequency (Harmonic) ni
defining formulation dp "$\begin{align} p&=&\frac{1}{\sqrt{\gamma}\hbar}P \\ \gamma&=&\frac{2 \pi c \omega}{\hbar} \end{align}$"^^La Te X ep
in defining formulation dp "$P$, Normal Mode Momentum"^^La Te X ep
in defining formulation dp "$\hbar$, Planck Constant"^^La Te X ep
in defining formulation dp "$\omega$, Vibration Frequency (Harmonic)"^^La Te X ep
in defining formulation dp "$c$, Speed of Light"^^La Te X ep
in defining formulation dp "$p$, Normal Mode Momentum (Dimensionless)"^^La Te X ep
description ap "dimensionless canonical momenta, corresponding to the normal mode coordinates used for the description of vibrations of many-body systems, e.g. molecules"@en

Normal Modesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NormalModes

These coordinates can be constructed by means of the GF (or FG) method by Wilson.
belongs to
Mathematical Model c
has facts
contains formulation op Quantum Hamiltonian (Normal Mode) ni
generalizes model op Normal Modes (Anharmonic) ni
generalizes model op Normal Modes (Harmonic) ni
generalizes model op Normal Modes (Intermolecular) ni
description ap "describing molecular (or other) vibrations of many-body systems in terms of normal modes"
wikidata I D ap Q3333538 ep

Normal Modes (Anharmonic)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NormalModesAnharmonic

Describing molecular (or other) vibrations of many-body systems in terms of normal modes, beyond the harmonic approximation
belongs to
Mathematical Model c
has facts
contains formulation op Quantum Eigen Energy (Anharmonic) ni
contains formulation op Quantum Hamiltonian (Normal Mode, Anharmonic) ni
generalizes model op Normal Modes (Harmonic) ni

Normal Modes (Harmonic)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NormalModesHarmonic

belongs to
Mathematical Model c
has facts
contains formulation op Quantum Eigen Energy (Harmonic) ni
contains formulation op Quantum Hamiltonian (Normal Mode, Harmonic) ni
description ap "describing molecular vibrations of many-body systems in terms of normal modes, within the harmonic approximation"@en

Normal Modes (Intermolecular)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NormalModesIntermolecular

thus describing cluster effects, solvent effects etc.
belongs to
Mathematical Model c
has facts
contains formulation op Quantum Eigen Energy (Intermolecular) ni
contains formulation op Quantum Hamiltonian (Normal Mode, Intermolecular) ni
generalizes model op Normal Modes (Anharmonic) ni
description ap "describing molecular vibrations in terms of normal modes, beyond the harmonic approximation, and including intermolecular interactions"@en
doi I D ap tf9605600753 ep
doi I D ap zenodo.12805933 ep

Normal Stressni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NormalStress

belongs to
Quantity c
has facts
description ap "force component perpendicular to a surface element divided by the area of that surface element"@en
qudt I D ap Normal Stress ep
wikidata I D ap Q11425837 ep

Number (Dimensionless)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NumberDimensionless

mathematical object used to count, label, and measure
belongs to
Quantity Kind c
has facts
is dimensionless dp "true"^^boolean
wikidata I D ap Q11563 ep

Number of Citiesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NumberOfCities

belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
description ap "number of cities in region m or n"@en

Number Of Exposed Individualsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NumberOfExposedIndividuals

belongs to
Quantity c
has facts
description ap "number of exposed individuals"@en

Number Of Exposed Individuals Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NumberOfExposedIndividualsFormulation

belongs to
Mathematical Formulation c
has facts
contained as formulation in op PDE SEIR Model ni
contains quantity op Coefficient Scaling Infectious To Exposed ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Exposed Individuals ni
defining formulation dp "$\hat{\mathcal{E}}^{(l)} = \Sigma_{\mathcal{E}} \hat{\mathcal{I}}^{(l)}$"^^La Te X ep
in defining formulation dp "$\Sigma_{\mathcal{E}}$, Coefficient Scaling Infectious To Exposed"^^La Te X ep
in defining formulation dp "$\hat{\mathcal{E}}^{(l)}$, Number Of Exposed Individuals"^^La Te X ep
in defining formulation dp "$\hat{\mathcal{I}}^{(l)}$, Number Of Infectious Individuals"^^La Te X ep

Number Of Individuals Tends To Infinity Assumptionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NumberOfIndividualsTendsToInfinityAssumption

belongs to
Mathematical Formulation c
has facts
contains quantity op Total Number Of Individuals ni
defining formulation dp "$N \rightarrow \inf$"^^La Te X ep
in defining formulation dp "$N$, Total Number Of Individuals"^^La Te X ep

Number Of Infected Citiesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NumberOfInfectedCities

belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
description ap "number of infected cities in region m or n at time t"@en

Number Of Infectious Individualsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#InfectiousIndividuals

The number of infectious individuals. These are individuals who have been infected and are capable of infecting susceptible individuals. I^i denotes the infectious Individuals in the ith subpopulation. if no i is provided, then it is a single-population model.
belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
description ap "number of infectious individuals"@en

Number of Object Propertiesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NumberOfObjectProperties

belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
description ap "number of object properties"@en

Number of Objectsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NumberOfObjects

belongs to
Quantity c
has facts
generalized by quantity op Integer Number (Dimensionless) ni
is dimensionless dp "true"^^boolean
description ap "number of objects"@en

Number Of Occurrencesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NumberOfOccurrences

e.g., number of events occurring in a fixed interval of time
belongs to
Quantity c
has facts
generalized by quantity op Integer Number (Dimensionless) ni
is dimensionless dp "true"^^boolean
description ap "count of how many times a specific event, value, or element appears within a given context or dataset"@en

Number of Particlesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NumberOfParticles

e.g. the number of atoms in a molecule
belongs to
Quantity c
has facts
generalized by quantity op Integer Number (Dimensionless) ni
is dimensionless dp "true"^^boolean
description ap "number of constituent particles in that system"@en

Number of Regionsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NumberOfRegions

belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
description ap "number of regions"@en

Number Of Removed Individualsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RemovedIndividuals

number of Removed/Recovered Individuals R^i denotes the removed Individuals in the ith subpopulation. if no i is provided, then it is a single-population model.
belongs to
Quantity c
has facts
generalized by op Removed ni
is dimensionless dp "true"^^boolean
description ap "number of removed/recovered individuals"@en

Number Of Susceptible Citiesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NumberOfSusceptibleCities

belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
description ap "number of susceptible cities in region m at time t"@en

Number Of Susceptible Individualsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SusceptibleIndividuals

The number of susceptible individuals. When a susceptible and an infectious individual come into "infectious contact", the susceptible individual contracts the disease and transitions to the infectious compartment. In the PDE SEIR Model subscript l denotes the lth subdomain. S^i denotes the susceptible Individuals in the ith subpopulation. if no i is provided, then it is a single-population model.
belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
description ap "number of susceptible individuals"@en

Number Of Susceptible Individuals Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NumberOfSusceptibleIndividualsFormulation

belongs to
Mathematical Formulation c
has facts
contained as formulation in op PDE SEIR Model ni
contains quantity op Coefficient Scaling Infectious To Exposed ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Removed Individuals ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Total Population Size ni
defining formulation dp "$$ \hat{\mathcal{S}}^{(l)} = \hat{\mathcal{N}}^{(l)} - (1 + \Sigma_{\mathcal{E}}) \hat{\mathcal{I}}^{(l)} - \hat{\mathcal{R}}^{(l)} $$"^^La Te X ep
in defining formulation dp "$\Sigma_{\mathcal{E}}}$, Coefficient Scaling Infectious To Exposed"^^La Te X ep
in defining formulation dp "$\hat{\mathcal{I}}^{(l)}$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$\hat{\mathcal{N}}^{(l)}$, Total Population Size"^^La Te X ep
in defining formulation dp "$\hat{\mathcal{R}}^{(l)}$, Number Of Removed Individuals"^^La Te X ep
in defining formulation dp "$\hat{\mathcal{S}}^{(l)}$, Number Of Susceptible Individuals"^^La Te X ep

Number of Time Pointsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#NumberOfTimepoints

belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
description ap "total number of time points at which observation were made"@en

Objectni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Object

anything that may be observed or acted upon by a subject
belongs to
Quantity Kind c
has facts
is dimensionless dp "true"^^boolean
wikidata I D ap Q488383 ep

Object Cluster Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ObjectClusterFormulation

belongs to
Mathematical Formulation c
has facts
contains quantity op Object Cluster Matrix ni
contains quantity op Object Committor Functions ni
contains quantity op Object Rating Matrix ni
defining formulation dp "$\mathrm{R_c} = (\chi^T\chi)^{-1}\chi^T\mathrm{R}\chi$"^^La Te X ep
in defining formulation dp "$\chi$, Object Committor Functions"^^La Te X ep
in defining formulation dp "$\mathrm{R_c}$, Object Cluster Matrix"^^La Te X ep
in defining formulation dp "$\mathrm{R}$, Object Rating Matrix"^^La Te X ep
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean
description ap "formulation determining the coherence of object clusters"@en

Object Cluster Matrixni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ObjectClusterMatrix

belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
description ap "matrix giving insight into the coherence of object clusters"@en

Object Committor Function Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ObjectCommittorFunctionFormulation

belongs to
Mathematical Formulation c
has facts
contains quantity op Object Committor Functions ni
contains quantity op Second Eigenvalue of Orthogonal Matrix ni
defining formulation dp "$\chi = [u*_2, 1 - u*_2]$"^^La Te X ep
in defining formulation dp "$\chi$, Object Committor Functions"^^La Te X ep
in defining formulation dp "$u*_2$, Second Eigenvalue of Orthogonal Matrix"^^La Te X ep
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean
description ap "formulation determining the object commitor functions"@en

Object Committor Functionsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ObjectCommittorFunctions

belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
description ap "non-negative vectors whose values correspond to the probability to end up in some property when starting the process in some object"@en

Object Commonality Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ObjectCommonalityFormulation

belongs to
Mathematical Formulation c
has facts
contains quantity op Number of Objects ni
contains quantity op Object ni
contains quantity op Object Commonality Matrix ni
contains quantity op Object Property ni
defining formulation dp "$M_{i,j} = f(o_i) \odot f(o_j) for i,j in N$"^^La Te X ep
in defining formulation dp "$N$, Number of Objects"^^La Te X ep
in defining formulation dp "$\mathbf{M}$,Object Commonality Matrix"^^La Te X ep
in defining formulation dp "$f(o)$, Object Property"^^La Te X ep
in defining formulation dp "$o$, Object"^^La Te X ep
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean
description ap "function defining the entries in the object commonality matrix"@en

Object Commonality Matrixni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ObjectCommonalityMatrix

belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
description ap "matrix containing object property commonalities of all object pairs"@en

Object Comparison Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ObjectComparisonFormulation

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Object Comparison Model ni
contains quantity op Boolean Ring ni
contains quantity op Number of Object Properties ni
contains quantity op Object Property ni
contains quantity op Power Set ni
defining formulation dp "$\mathcal{B} = \mathcal{P}(x_1,x_2,...,x_m)$"^^La Te X ep
in defining formulation dp "$\mathcal{B}$, Boolean Ring"^^La Te X ep
in defining formulation dp "$\mathcal{P}$, Power Set"^^La Te X ep
in defining formulation dp "$m$, Number of Object Properties"^^La Te X ep
in defining formulation dp "$x$, Object Property"^^La Te X ep
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean
description ap "Boolean ring over m object properties"@en

Object Comparison Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ObjectComparisonModel

belongs to
Mathematical Model c
has facts
models op Identify destruction rules in ancient egyptian objects ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean
description ap "mathematical model comparing objects using a boolean ring over the object properties"@en

Object Propertyni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ObjectProperty

belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
description ap "property of an object"@en

Object Rating Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ObjectRatingFormulation

belongs to
Mathematical Formulation c
has facts
contains quantity op Maximal Object Descriptiveness Rating ni
contains quantity op Object Commonality Matrix ni
contains quantity op Object Rating Matrix ni
defining formulation dp "$f: \mathbf{M}\rightarrow\mathbf{R}: f(s)=y, \ s\in\mathbf{M},\ y\in\{\mathbf{R}| 0 \leq y \leq score_{max}\}$"^^La Te X ep
in defining formulation dp "$\mathbf{M}$, Object Commonality Matrix"^^La Te X ep
in defining formulation dp "$\mathbf{R}$, Object Rating Matrix"^^La Te X ep
in defining formulation dp "$score_{max}$, Maximal Object Descriptiveness Rating"^^La Te X ep
is convex dp "false"^^boolean
is deterministic dp "false"^^boolean
is dimensionless dp "true"^^boolean
is dynamic dp "false"^^boolean
description ap "formulation rating the object commonalities"@en

Object Rating Matrixni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ObjectRatingMatrix

belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
description ap "matrix rating the descriptiveness of the object commonalities"@en

Object Rating Matrix Decomposition (Schur)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ObjectRatingMatrixDecompositionSchur

belongs to
Mathematical Formulation c
has facts
contains quantity op Object Rating Matrix ni
contains quantity op Orthogonal Matrix ni
contains quantity op Upper-Triangular Matrix ni
defining formulation dp "$\mathbf{R} = \mathbf{U}\mathbf{V}\mathbf{U^T}$"^^La Te X ep
in defining formulation dp "$\mathbf{R}$, Object Rating Matrix"^^La Te X ep
in defining formulation dp "$\mathbf{U}$, Orthogonal Matrix"^^La Te X ep
in defining formulation dp "$\mathbf{V}$, Upper-Triangular Matrix"^^La Te X ep
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean
is dynamic dp "false"^^boolean
description ap "Schur decomposition of the object rating matrix"@en
wikidata I D ap Q1064218 ep

Ohm Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OhmEquation

Note that the formulation used here is a generalization of the well-known R=U/I.
belongs to
Mathematical Formulation c
has facts
contains quantity op Electric Conductivity ni
contains quantity op Electric Current Density ni
contains quantity op Electric Field ni
defining formulation dp "$J=\sigma E$"^^La Te X ep
in defining formulation dp "$E$, Electric Field"^^La Te X ep
in defining formulation dp "$J$, Electric Current Density"^^La Te X ep
in defining formulation dp "$\sigma$, Electric Conductivity"^^La Te X ep
description ap "Ohm's law for transport of electric charge"@en
wikidata I D ap Q41591 ep

Oosterhout (2024) Finite-strain poro-visco-elasticity with degenerate mobilityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Oosterhout_2024_Finite-strain_poro-visco-elasticity_with_degenerate_mobility

belongs to
Publication c
has facts
doi I D ap zamm.202300486 ep

Opinionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Opinion

Opinion of a given individual at a given time, lying in a d-dimensional opinion space $D \subset \mathbb{R}^d$. x, y and z represent Individuals', media's and Influencer's opinions respectively
belongs to
Quantity c
has facts
generalized by quantity op Opinion Vector of Individuals ni
generalized by quantity op Opinion Vector of Influencers ni
generalized by quantity op Opinion Vector of Media ni
description ap "opinion of a given individual at a given time"@en
wikidata I D ap Q3962655 ep

Opinion Dynamicsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OpinionDynamics

belongs to
Research Problem c
has facts
contained in field op Computational Social Science ni
description ap "modelling opinion dynamics under the impact of influencer and media strategies"@en

Opinion Model With Influencers And Mediani back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OpinionModelWithInfluencersAndMedia

General opinion model resulting from a large number of individuals adapting their opinions through interaction with each other as well as due to the influence of a few specific agents with particular roles, namely traditional media and social media influencers.
belongs to
Mathematical Model c
has facts
models op Opinion Dynamics ni
is space-continuous dp "true"^^boolean
is time-continuous dp "true"^^boolean
description ap "general opinion model considering individuals, traditional media and social media influencers"@en

Opinion Vector of Individualsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OpinionVectorOfIndividuals

vector containing N opinions for N Individuals, Each opinion $x_i(t)$ lies in a a continuous d-dimensional opinion space $D \subset \mathbb{R}^d$|. Subscript denotes the individual
belongs to
Quantity c
has facts
description ap "vector containing N opinions for N Individuals"@en

Opinion Vector of Influencersni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OpinionVectorOfInfluencers

vector containing L opinions for L Individuals, Each opinion $z_l(t)$ lies in a a continuous d-dimensional opinion space $D \subset \mathbb{R}^d$
belongs to
Quantity c
has facts
description ap "vector containing L opinions for L Individuals"@en

Opinion Vector of Mediani back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OpinionVectorOfMedia

vector containing M opinions for M Individuals, Each opinion $y_m(t)$ lies in a a continuous d-dimensional opinion space $D \subset \mathbb{R}^d$
belongs to
Quantity c
has facts
description ap "vector containing M opinions for M Individuals"@en

Optimal Controlni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OptimalControl

Finding controls, e.g. external forces|fields, such that they drive a given control system from a given initial state to a specific final state (target), typically with constraints such as using not too high fields (cost).
belongs to
Computational Task c
has facts
applies model op Control System Model (Bilinear) ni
applies model op Electron Shuttling Model ni
applies model op Quantum Model (Closed System) ni
applies model op Quantum Model (Open System) ni
contains final condition op Optimal Control Final ni
contains formulation op Optimal Control Backward ni
contains formulation op Optimal Control Forward ni
contains formulation op Optimal Control Update ni
contains initial condition op Optimal Control Initial ni
contains objective op Optimal Control Cost ni
contains objective op Optimal Control Target ni
contains output op Control System Input ni
description ap "branch of control theory that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized"@en
arxiv I D ap 0707.1883 ep
doi I D ap j.cpc.2018.02.022 ep
doi I D ap R01 ep
wikidata I D ap Q1971426 ep

Optimal Control Backwardni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OptimalControlBackward

belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Input ni
contains quantity op Control System Lagrange Multiplier ni
contains quantity op Control System Matrix A ni
contains quantity op Control System Matrix B ni
contains quantity op Control System Matrix N ni
contains quantity op Time ni
defining formulation dp "$\dot{z}(t)=-(A^{\dag}+ \sum_ku_k(t)N^{\dag}_k)z(t)-B^{\dag}u(t)$"^^La Te X ep
in defining formulation dp "$A$, Control System Matrix A"^^La Te X ep
in defining formulation dp "$B$, Control System Matrix B"^^La Te X ep
in defining formulation dp "$N$, Control System Matrix N"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$u$, Control System Input"^^La Te X ep
in defining formulation dp "$z$, Control System Lagrange Multiplier"^^La Te X ep
description ap "Lagrange multipliers of control systems are propagated backward via the adjoint of the input equation"@en

Optimal Control Constraintni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OptimalControlConstraint

belongs to
Mathematical Formulation c
has facts
contained as constraint condition in op Optimal Control ni
contains quantity op Control System Duration ni
contains quantity op Control System Input ni
contains quantity op Control System Lagrange Multiplier ni
contains quantity op Control System Matrix A ni
contains quantity op Control System Matrix N ni
contains quantity op Control System State ni
contains quantity op Time ni
defining formulation dp "$J[u,x,z]=2\Re\int_0^Tdtz^{\dag}(t)\left(\partial_t-A-\sum_ku_k(t)N_k\right)x(t)$"^^La Te X ep
in defining formulation dp "$A$, Control System Matrix A"^^La Te X ep
in defining formulation dp "$N$, Control System Matrix N"^^La Te X ep
in defining formulation dp "$T$, Control System Duration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$u$, Control System Input"^^La Te X ep
in defining formulation dp "$x$, Control System State"^^La Te X ep
in defining formulation dp "$z$, Control System Lagrange Multiplier"^^La Te X ep
description ap "Constraint functional in optimal control systems requiring that the system's state vector follows the respective equation of motion"@en

Optimal Control Costni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OptimalControlCost

Minimizes the cost of the control of a system, e.g. minimize the fluence of a laser field
belongs to
Quantity c
has facts
description ap "cost functional in optimal control"@en

Optimal Control Cost (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OptimalControlCostDefinition

Minimizes the cost of the control of a system, e.g. minimize the fluence of a laser field
belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Duration ni
contains quantity op Control System Input ni
contains quantity op Optimal Control Cost ni
contains quantity op Optimal Control Penalty Factor ni
contains quantity op Time ni
defines op Optimal Control Cost ni
defining formulation dp "$J[u] \equiv \sum_k\alpha_k\int_0^Tdtu_k^2(t)$"^^La Te X ep
in defining formulation dp "$J$, Optimal Control Cost"^^La Te X ep
in defining formulation dp "$T$, Control System Duration"^^La Te X ep
in defining formulation dp "$\alpha$, Optimal Control Penalty Factor"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$u$, Control System Input"^^La Te X ep
description ap "cost functional in optimal control"@en

Optimal Control Finalni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OptimalControlFinal

belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Duration ni
contains quantity op Control System Lagrange Multiplier ni
contains quantity op Control System Matrix D ni
contains quantity op Control System State ni
contains quantity op Time ni
defining formulation dp "$z(t=T)$=Dx(t=T)$"^^La Te X ep
in defining formulation dp "$D$, Control System Matrix D"^^La Te X ep
in defining formulation dp "$T$, Control System Duration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$x$, Control System State"^^La Te X ep
in defining formulation dp "$z$, Control System Lagrange Multiplier"^^La Te X ep
description ap "final condition for the (backward) propagation of the Lagrange multiplier of a control system"@en

Optimal Control Forwardni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OptimalControlForward

belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Input ni
contains quantity op Control System Matrix A ni
contains quantity op Control System Matrix B ni
contains quantity op Control System Matrix N ni
contains quantity op Control System State ni
contains quantity op Time ni
defining formulation dp "$\dot{x}(t)=(A+ \sum_ku_k(t)N_k)x(t)+Bu(t)$"^^La Te X ep
in defining formulation dp "$A$, Control System Matrix A"^^La Te X ep
in defining formulation dp "$B$, Control System Matrix B"^^La Te X ep
in defining formulation dp "$N$, Control System Matrix N"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$u$, Control System Input"^^La Te X ep
in defining formulation dp "$x$, Control System State"^^La Te X ep
description ap "state vectors of control systems are propagated forward via the input equation"@en

Optimal Control Initialni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OptimalControlInitial

belongs to
Mathematical Formulation c
has facts
contains formulation op Initial Control State ni
contains quantity op Control System State ni
contains quantity op Time ni
defining formulation dp "$x(t=0)=x_0$"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$x$, Control System State"^^La Te X ep
in defining formulation dp "$x_0$, Initial Control State"^^La Te X ep
description ap "initial condition for the (forward) propagation of the state vector of a control system"@en

Optimal Control Penalty Factorni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OptimalControlPenaltyFactor

In optrimal control theory, a penalty factor can be used to balance between the two objectives: maximizing the target function[al] versus minimizing the cost function[al]
belongs to
Quantity c
has facts
description ap "used to balance between the two objectives: maximizing the target function[al] versus minimizing the cost function[al]"@en

Optimal Control Targetni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OptimalControlTarget

Maximize the quadratic output of a given control system
belongs to
Quantity c
has facts
description ap "target functional in optimal control"@en

Optimal Control Target (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OptimalControlTargetDefinition

Maximize the quadratic output of a given control system
belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Duration ni
contains quantity op Control System Input ni
contains quantity op Control System Matrix D ni
contains quantity op Control System State ni
contains quantity op Optimal Control Target ni
defines op Optimal Control Target ni
defining formulation dp "$J[u,x] \equiv x^{\dag}(T)Dx(T)$"^^La Te X ep
in defining formulation dp "$D$, Control System Matrix D"^^La Te X ep
in defining formulation dp "$J$, Optimal Control Target"^^La Te X ep
in defining formulation dp "$T$, Control System Duration"^^La Te X ep
in defining formulation dp "$u$, Control System Input"^^La Te X ep
in defining formulation dp "$x$, Control System State"^^La Te X ep
description ap "target functional in optimal control"@en

Optimal Control Updateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OptimalControlUpdate

belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Input ni
contains quantity op Control System Lagrange Multiplier ni
contains quantity op Control System Matrix N ni
contains quantity op Control System State ni
contains quantity op Optimal Control Penalty Factor ni
contains quantity op Time ni
defining formulation dp "$u_k(t)=-\frac{1}{\alpha_k}\Im\left(z^{\dag}(t)N_kx(t) \right)$"^^La Te X ep
in defining formulation dp "$N$, Control System Matrix N"^^La Te X ep
in defining formulation dp "$\alpha$, Optimal Control Penalty Factor"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$u$, Control System Input"^^La Te X ep
in defining formulation dp "$x$, Control System State"^^La Te X ep
in defining formulation dp "$z$, Control System Lagrange Multiplier"^^La Te X ep
description ap "updated control is calculated from state vector and Lagrange multiplier of a control system"@en

Optimization in Public Transportationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OptimizationInPublicTransportation

belongs to
Research Field c

Origin Destination Datani back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OriginDestinationData

belongs to
Quantity c
has facts
description ap "data including, amongst others, information from which origin to which destination passengers travel and which mode of transport they use"@en

Orthogonal Matrixni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OrthogonalMatrix

belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
description ap "real square matrix whose columns and rows are orthogonal unit vectors"@en
wikidata I D ap Q333871 ep

Overall Distribution Of Individualsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OverallDistributionOfIndividuals

belongs to
Quantity c
has facts
description ap "pattern or arrangement of individuals within a population across a given area or space"@en

Overall Distribution Of Individuals Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#OverallDistributionOfIndividualsFormulation

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Partial Mean Field Opinion Model ni
contains quantity op Limiting Distribution Of Individuals ni
contains quantity op Overall Distribution Of Individuals ni
defining formulation dp "$\rho = \Sigma_{m,l} \rho_{m,l}$"^^La Te X ep
in defining formulation dp "$\rho$, Overall Distribution Of Individuals"^^La Te X ep
in defining formulation dp "$rho_{m,l}$, Limiting Distribution Of Individuals"^^La Te X ep

Pair Functionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PairFunction

Non-negative pair function used to weight interaction between two individuals. Possible choices are $\phi = exp(-x)$ that places exponentially more weight on close-by individuals or $\phi = 1$ as in the DeGroot model resulting in interactions irrespective of the opinion distance between individuals.
belongs to
Quantity c
has facts
description ap "non-negative pair function used to weight interaction between two individuals"@en

Pair Function Assumptionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PairFunctionAssumption

This pair function places exponentially more weight on close-by individuals. Implies that individuals that are already close in opinion space excert higher social influence on each other (homophily)
belongs to
Mathematical Formulation c
has facts
contained as assumption in op Opinion Model With Influencers And Media ni
contains quantity op Pair Function ni
defines op Pair Function ni
defining formulation dp "$\phi(x) = exp(-x)$"^^La Te X ep
in defining formulation dp "$\phi(x)$, Pair Function"^^La Te X ep
is space-continuous dp "true"^^boolean

Parameter Estimation of Enzyme Kineticsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ParameterEstimationOfEnzymeKinetics

belongs to
Computational Task c
has facts
generalizes task op Linear Parameter Estimation of Enzyme Kinetics ni
generalizes task op Nonlinear Parameter Estimation of Enzyme Kinetics ni
description ap "determination of the kinetic constants for enzyme-catalyzed reactions"@en
doi I D ap B978 0 12 801238 3.05143 6 ep

Parameter To Scale Attractive Force From Influencersni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ParameterToScaleAttractiveForceFromInfluencers

belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
description ap "parameter to scale attractive force from influencers"@en

Parameter To Scale Attractive Force From Mediani back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ParameterToScaleAttractiveForceFromMedia

belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
description ap "parameter to scale attractive force from media"@en

Parameter To Scale Attractive Force From Other Individualsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ParameterToScaleAttractiveForceFromOtherIndividuals

belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
description ap "parameter to scale attractive force from other individuals"@en

Partial Mean Field Opinion Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PartialMeanFieldOpinionModel

For situations with many individuals but few influencers and media, one can derive the mean-field limit by a partial differential equation (PDE) that describes the opinion dynamics of individuals in the limit of infinitely many individuals but is usually already a good approximation to the dynamics for finitely many individuals. Since here the number of influencers and media is still small and finite, their dynamics are still best described by SDEs but now coupled to PDEs for the evolution of the opinion distributions of individuals.
belongs to
Mathematical Model c
has facts
models op Opinion Dynamics ni
description ap "opinion model considering many individuals and few traditional media and social media influencers"@en

Particle Flux Densityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ParticleFluxDensity

Particle Flux Density
belongs to
Quantity c
has facts
description ap "time derivative of particle fluence"@en
alt Label ap "Fluence Rate"@en
alt Label ap "Particle Fluence Rate"@en
alt Label ap "Time Derivative of Particle Fluence"@en
wikidata I D ap Q98497410 ep

Particle Number Densityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ParticleNumberDensity

belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
description ap "number of particles per volume"@en
wikidata I D ap Q98601569 ep

Particles In Electromagnetic Fieldsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ParticlesInElectroMagneticFields

belongs to
Research Problem c
has facts
contained in field op Electromagnetism ni
description ap "motion of charged particles subject to an electric and/or magnetic fields, e.g. in a cathode ray tube, in an ion trap, or in a mass spectrometer"@en

Passive Muscle Forceni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PassiveMuscleForce

belongs to
Quantity c
has facts
defined by op Passive Muscle Force (Definition) ni
description ap "force developed in noncontracting or inactive muscles by the elastic elements within the muscle"@en

Passive Muscle Force (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Passive_Muscle_Force

belongs to
Mathematical Formulation c
has facts
contains quantity op Maximum Isometric Muscle Force ni
contains quantity op Muscle Length ni
contains quantity op Passive Muscle Force ni
contains quantity op Passive Muscle Strain ni
contains quantity op Stress Free Muscle Length ni
contains quantity op Time ni
defining formulation dp "$$F_{\text{PME}}(\mathcal{l}_{\text{M}}) \equiv F^\text{M}_0 \cdot \frac{\exp\left(\frac{k_{\text{PE}}}{\epsilon^{\text{M}}_0}\left(\frac{\mathcal{l_{\text{M}}(t)}}{\mathcal{l}_{\text{M}}^{\text{slack}}}-1\right)\right)-1}{\exp(k_{\text{PE}})-1}$$"^^La Te X ep
in defining formulation dp "$F^{\text{M}}_0$, Maximum Isometric Muscle Force"^^La Te X ep
in defining formulation dp "$F_{\text{PME}}$, Passive Muscle Force"^^La Te X ep
in defining formulation dp "$\epsilon^{M}_0$, Passive Muscle Strain"^^La Te X ep
in defining formulation dp "$\mathcal{l}^{\text{slack}}_{\text{M}}$, Stress Free Muscle Length"^^La Te X ep
in defining formulation dp "$\mathcal{l}_{\text{M}}$, Muscle Length"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
description ap "force developed in noncontracting or inactive muscles by the elastic elements within the muscle"@en

Passive Muscle Strainni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PassiveMuscleStrain

belongs to
Quantity c
has facts
generalized by quantity op Mechanical Strain ni
description ap "passive muscle strain"@en

Passive Tendon Forceni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PassiveTendonForce

concrete values are fitted on experimental studies from doi:10.5194/ms-7-19-2016
belongs to
Quantity c
has facts
defined by op Passive Tendon Force (Definition) ni
description ap "force that a tendon can generate without the muscle actively contracting"@en

Passive Tendon Force (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Passive_Tendon_Force

belongs to
Mathematical Formulation c
has facts
contains quantity op Maximum Isometric Muscle Force ni
contains quantity op Passive Tendon Force ni
contains quantity op Tendon Length ni
contains quantity op Tendon Strain ni
defines op Passive Tendon Force ni
defining formulation dp "$$F_{\text{PTE}}(\mathcal{l}_{\text{T}}(t)) \equiv \begin{cases} F_0^{\text{M}} \cdot0.10377(\exp(91-\epsilon_{\text{T}}(t))-1) ~ & \text{if$\leq \epsilon_{\text{T}}(t)\leq 0.01516$ } \\ F_0^{\text{M}} \cdot (37.526 \cdot \epsilon_{\text{T}}(t) - 0.26029 ) ~ & \text{if $0.01516 <\epsilon_{\text{T}}(t) < 0.1 $} \end{cases}$$"^^La Te X ep
in defining formulation dp "$F_0^{\text{M}}$, Maximum Isometric Muscle Force"^^La Te X ep
in defining formulation dp "$F_{\text{PTE}}$, Passive Tendon Force"^^La Te X ep
in defining formulation dp "$\epsilon_{\text{T}}$, Tendon Strain"^^La Te X ep
in defining formulation dp "$\mathcal{l}_{\text{T}}$, Tendon Length"^^La Te X ep
description ap "force that a tendon can generate without the muscle actively contracting"@en

PDE SEIR Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#HybridPDEODESEIRModel

Spatial spreading model of SEIR(Susceptible, Exposed, Infectious, and Removed) type in a domain $\Omega \subset \mathbb{R}^2$ modeling both the SEIR dynamics and spatial diffusion of infectious individuals. Employing Partial differential equations.
belongs to
Mathematical Model c
has facts
models op Spreading of Infectious Diseases ni
description ap "spatial spreading model of susceptible, exposed, infectious, and removed individuals"@en

Period Lengthni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PeriodLength

belongs to
Quantity c
has facts
generalized by quantity op Time ni
description ap "length of a period in time units"@en

Periodic Boundary Condition For Electric Potentialni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PeriodicBoundaryConditionElectricField

Example: The SiQbus electron shuttling device contains periodically repeated unit cells with four clavier gates each.
belongs to
Mathematical Formulation c
has facts
contains quantity op Electric Potential ni
contains quantity op Length Of Unit Cell ni
contains quantity op Time ni
generalized by formulation op Periodic Boundary Conditions ni
defining formulation dp "$\phi(r,t)=\phi(r+L,t)$"^^La Te X ep
in defining formulation dp "$L$, Length Of Unit Cell"^^La Te X ep
in defining formulation dp "$\phi$, Electric Potential"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
description ap "periodic boundary condition for electric potential, e.g., for modeling devices with repeated units"@en

Periodic Boundary Conditionsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PeriodicBoundaryConditions

When an object passes through one side of the unit cell, it re-appears on the opposite side with the same velocity. In topological terms, the space made by one-dimensional PBCs can be thought of as being mapped onto a circle. The space made by two-dimensional PBCs can be thought of as being mapped onto a torus.
belongs to
Mathematical Formulation c
has facts
description ap "set of boundary conditions which are often chosen for approximating a large (infinite) system by using a small part called a unit cell"@en
wikidata I D ap Q2992284 ep

Permeability (Vacuum)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PermeabilityVacuum

The magnetic permeability in a classical vacuum. It is a physical constant, conventionally written as μ0 (pronounced "mu nought" or "mu zero"). It quantifies the strength of the magnetic field induced by an electric current.
belongs to
Quantity c
is same as
Magnetic Constant ni
has facts
description ap "strength of the magnetic field induced by an electric current"@en
qudt I D ap Magnetic Constant ep
wikidata I D ap Q1515261 ep

Permittivity (Dielectric)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PermittivityDielectric

In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter epsilon, is a measure of the electric polarizability of a dielectric material. It is given as the product of the vacuum dielectric permittivity and the relative permittivity of the material. Permittivities may be complex and frequency-dependent.
belongs to
Quantity c
has facts
description ap "measure of the electric polarizability of a dielectric material"@en
qudt I D ap Permittivity ep
wikidata I D ap Q211569 ep

Permittivity (Relative)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PermittivityRelative

The relative permittivity (in older texts, dielectric constant) is the permittivity of a material expressed as a ratio with the electric permittivity of a vacuum. A dielectric is an insulating material, and the dielectric constant of an insulator measures the ability of the insulator to store electric energy in an electrical field. Permittivities may be complex and frequency-dependent.
belongs to
Quantity c
has facts
defined by op Permittivity (Relative, Definition) ni
nondimensionalizes quantity op Permittivity (Dielectric) ni
description ap "permittivity of a material expressed as a ratio with the electric permittivity of a vacuum"@en
wikidata I D ap Q4027242 ep

Permittivity (Relative, Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PermittivityRelativeDefinition

The relative permittivity (in older texts, dielectric constant) is the permittivity of a material expressed as a ratio with the electric permittivity of a vacuum. A dielectric is an insulating material, and the dielectric constant of an insulator measures the ability of the insulator to store electric energy in an electrical field. Permittivities may be complex and frequency-dependent.
belongs to
Mathematical Formulation c
has facts
contains quantity op Permittivity (Dielectric) ni
contains quantity op Permittivity (Relative) ni
contains quantity op Permittivity (Vacuum) ni
defining formulation dp "$\varepsilon_{\mathrm{r}} \equiv \frac{\varepsilon}{\varepsilon_0}$"^^La Te X ep
in defining formulation dp "$\varepsilon$, Permittivity (Dielectric)"^^La Te X ep
in defining formulation dp "$\varepsilon_0$, Permittivity (Vacuum)"^^La Te X ep
in defining formulation dp "$\varepsilon_{\mathrm{r}}$, Permittivity (Relative)"^^La Te X ep
description ap "permittivity of a material expressed as a ratio with the electric permittivity of a vacuum"@en
wikidata I D ap Q4027242 ep

Permittivity (Vacuum)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PermittivityVacuum

Vacuum permittivity is the value of the absolute dielectric permittivity of classical vacuum. It may also be referred to as the permittivity of free space, the electric constant, or the distributed capacitance of the vacuum. It is an ideal (baseline) physical constant.
belongs to
Quantity c
is same as
Electric Constant ni
has facts
generalized by quantity op Permittivity (Dielectric) ni
description ap "physical constant that represents the capability of the vacuum to permit electric field lines"@en
qudt I D ap Electric Constant ep
wikidata I D ap Q6158 ep

Physical Chemistryni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PhysicalChemistry

Note that the distinction between Physical Chemistry and Chemical Physics is not always straight-forward to define.
belongs to
Research Field c
has facts
contains problem op Molecular Reaction Dynamics ni
contains problem op Molecular Spectroscopy (Transient) ni
description ap "subdiscipline at the intersection of physics and chemistry, describing chemical concepts utilizing the principles of physics"
mardi I D ap Item: Q133773 ep
wikidata I D ap Q11372 ep

Pi Numberni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PiNumber

belongs to
Quantity c
has facts
description ap "ratio of circumference and the diameter of a circle"@en
wikidata I D ap Q167 ep

Planck Constantni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PlanckConstant

a physical constant that is the quantum of action in quantum mechanics. The Planck constant was first described as the proportionality constant between the energy of a photon and the frequency of its associated electromagnetic wave.
belongs to
Quantity c
has facts
description ap "quantum of action in quantum mechanics"@en
qudt I D ap Planck Constant ep
wikidata I D ap Q122894 ep

Poisson Distributionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PoissonDistribution

Assuming that these events occur with a known constant mean rate and independently of the time since the last event
belongs to
Quantity c
has facts
generalized by quantity op Probability Distribution ni
description ap "discrete probability distribution that models the number of events occurring in a fixed interval of time or space, given a constant mean rate of occurrence"@en
wikidata I D ap Q205692 ep

Poisson Distribution (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PoissonDistributionDefinition

belongs to
Mathematical Formulation c
has facts
contains quantity op Euler Number ni
contains quantity op Expectation Value ni
contains quantity op Number Of Occurrences ni
contains quantity op Poisson Distribution ni
defines op Poisson Distribution ni
defining formulation dp "$P(k;\lambda)\sim\frac{\lambda^ke^{-\lambda}}{k!}$"^^La Te X ep
in defining formulation dp "$P$, Poisson Distribution"^^La Te X ep
in defining formulation dp "$\lambda$, Expectation Value"^^La Te X ep
in defining formulation dp "$e$, Euler Number"^^La Te X ep
in defining formulation dp "$k$, Number Of Occurrences"^^La Te X ep
description ap "discrete probability distribution that models the number of events occurring in a fixed interval of time or space, given a constant mean rate of occurrence"@en
wikidata I D ap Q205692 ep

Poisson Equation For The Electric Potentialni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PoissonEquationForTheElectricPotential

belongs to
Mathematical Formulation c
has facts
contains quantity op Density Of Electrons ni
contains quantity op Density Of Holes ni
contains quantity op Doping Profile ni
contains quantity op Electric Potential ni
contains quantity op Elementary Charge ni
contains quantity op Fermi Potential For Electrons ni
contains quantity op Fermi Potential For Holes ni
contains quantity op Permittivity (Dielectric) ni
defining formulation dp "$-\nabla\cdot\left(\epsilon_s\nabla\psi\right) = q\left(C+p(\psi,\phi_p)-n(\psi,\phi_n)\right)$"^^La Te X ep
in defining formulation dp "$C$, Doping Profile"^^La Te X ep
in defining formulation dp "$\epsilon_s$, Permittivity (Dielectric)"^^La Te X ep
in defining formulation dp "$\phi_n$, Fermi Potential For Electrons"^^La Te X ep
in defining formulation dp "$\phi_p$, Fermi Potential For Holes"^^La Te X ep
in defining formulation dp "$\psi$, Electric Potential"^^La Te X ep
in defining formulation dp "$n$, Density Of Electrons"^^La Te X ep
in defining formulation dp "$p$, Density Of Holes"^^La Te X ep
in defining formulation dp "$q$, Elementary Charge"^^La Te X ep
is dynamic dp "false"^^boolean
is space-continuous dp "true"^^boolean
description ap "For use in semiconductor physics, with electron and hole densities"@en

Poisson Equation For The Electric Potential (Finite Volume)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PoissonEquationForTheElectricPotentialFiniteVolume

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Scharfetter-Gummel Scheme ni
contains quantity op Control Volume ni
contains quantity op Electric Potential ni
contains quantity op Permittivity (Dielectric) ni
discretizes formulation op Poisson Equation For The Electric Potential ni
defining formulation dp "$-\epsilon_s\left(\frac{\psi_{k+1}-\psi_{k}}{h_{k,k+1}}-\frac{\psi_{k}-\psi_{k-1}}{h_{k-1,k}}\right)=q\left(C_k+p(\psi_k,\phi_{p;k})-n(\psi_k,\phi_{n;k})\right)|\omega_k|$"^^La Te X ep
in defining formulation dp "$\epsilon_s$, Permittivity (Dielectric)"^^La Te X ep
in defining formulation dp "$\omega_k$, Control Volume"^^La Te X ep
in defining formulation dp "$\psi$, Electric Potential"^^La Te X ep
is space-continuous dp "false"^^boolean
description ap "Used within the Scharfetter-Gummel finite volume disretization scheme which is the standard numerical method for solving the van Roosbroeck system"@en

Poisson log-Likelihoodni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PoissonLogLikelihood

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Gamma-Gompertz-Makeham Model ni
contains quantity op Age Of An Individual ni
contains quantity op Death Count ni
contains quantity op Exposure Of An Individual ni
contains quantity op Likelihood Value ni
contains quantity op Risk Of Death ni
defining formulation dp "$\log L = \sum_{x}[D(x)\log\mu(x)-E(x)\mu(x)]$"^^La Te X ep
in defining formulation dp "$D$, Death Count"^^La Te X ep
in defining formulation dp "$E$, Exposure Of An Individual"^^La Te X ep
in defining formulation dp "$L$, Likelihood Value"^^La Te X ep
in defining formulation dp "$\mu$, Risk Of Death"^^La Te X ep
in defining formulation dp "$x$, Age Of An Individual"^^La Te X ep
description ap "log-likelihood function of a Poisson distribution"@en

Poisson-Distributed Deathsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PoissonDistributedDeaths

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Gamma-Gompertz-Makeham Model ni
contains quantity op Age Of An Individual ni
contains quantity op Death Count ni
contains quantity op Exposure Of An Individual ni
contains quantity op Poisson Distribution ni
contains quantity op Risk Of Death ni
defining formulation dp "$D(x)\sim P\left(E(x)\mu(x)\right)$"^^La Te X ep
in defining formulation dp "$D$, Death Count"^^La Te X ep
in defining formulation dp "$E$, Exposure Of An Individual"^^La Te X ep
in defining formulation dp "$P$, Poisson Distribution"^^La Te X ep
in defining formulation dp "$\mu$, Risk Of Death"^^La Te X ep
in defining formulation dp "$x$, Age Of An Individual"^^La Te X ep
description ap "Assuming that death counts at age x are Poisson-distributed"@en

Polar Angleni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PolarAngle

Angle in the spherical coordinate system in the range $0 < \theta < \pi$
belongs to
Quantity Kind c
has facts
wikidata I D ap Q116757614 ep

Pomologyni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Pomology

belongs to
Research Field c
has facts
contains problem op Gravitational Effects On Fruit ni
generalized by field op Biology ni
description ap "branch of botany that studies fruits and their cultivation"@en
wikidata I D ap Q35911 ep

Population Densityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PopulationDensity

Population density is a measure of the number of individuals per unit area, typically expressed as the number of individuals per square kilometer. It is used to study human and animal populations for various administrative and scientific purposes.
belongs to
Quantity c
has facts
description ap "measure of the number of individuals per unit area"@en

Poro-Visco-Elastic (Dirichlet Boundary)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PoroViscoElasticDirichletBoundary

belongs to
Mathematical Formulation c
has facts
contained as boundary condition in op Poro-Visco-Elastic Model ni
contains quantity op Mechanical Deformation ni
contains quantity op Mechanical Deformation (Boundary Value) ni
contains quantity op Spatial Variable ni
generalized by formulation op Dirichlet Boundary Condition ni
defining formulation dp "$\chi(t,x) = \chi_D(t,x)$"^^La Te X ep
in defining formulation dp "$\chi$, Mechanical Deformation"^^La Te X ep
in defining formulation dp "$\chi_D$, Mechanical Deformation (Boundary Value)"^^La Te X ep
in defining formulation dp "$x$, Spatial Variable"^^La Te X ep
description ap "Dirichlet boundary condition for mechanical deformation"@en

Poro-Visco-Elastic (Neumann Boundary)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PoroViscoElasticNeumannBoundary

belongs to
Mathematical Formulation c
has facts
contained as boundary condition in op Poro-Visco-Elastic Model ni
contains quantity op Concentration ni
contains quantity op Free Energy Density ni
contains quantity op Mechanical Deformation ni
contains quantity op Spatial Variable ni
contains quantity op Surface Force Density ni
contains quantity op Unit Normal Vector ni
contains quantity op Viscous Dissipation Potential ni
generalized by formulation op Neumann Boundary Condition ni
defining formulation dp "$(\partial_{\nabla \chi} \Phi(x,\nabla\chi(t,x),c(t,x)) + \partial_{\nabla\dot\chi}\zeta(x,\nabla\dot\chi(t,x),\nabla\chi(t,x),c(t,x)))\nu - \nabla_s\cdot (\partial_{D^2\chi} H(x,D^2\chi(t,x))\nu) = g(t,x)$"^^La Te X ep
in defining formulation dp "$\Phi$, Free Energy Density"^^La Te X ep
in defining formulation dp "$\chi$, Mechanical Deformation"^^La Te X ep
in defining formulation dp "$\nu$, Unit Normal Vector"^^La Te X ep
in defining formulation dp "$\zeta$, Viscous Dissipation Potential"^^La Te X ep
in defining formulation dp "$c$, Concentration"^^La Te X ep
in defining formulation dp "$g$, Surface Force Density"^^La Te X ep
in defining formulation dp "$x$, Spatial Variable"^^La Te X ep
description ap "Neumann boundary condition for mechanical deformation"@en

Poro-Visco-Elastic Diffusion Boundary Conditionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PoroViscoElasticDiffusionBoundaryCondition

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op External Chemical Potential ni
contains quantity op Fluid Intrinsic Permeability (Porous Medium) ni
contains quantity op Hydraulic Conductivity ni
contains quantity op Mechanical Deformation ni
defining formulation dp "$M(\nabla\chi,c)\nabla\partial_c\Phi(x,\nabla\chi,c)\cdot \nu = \kappa(x)(\mu_e(t,x)-\partial_c\Phi(x,\nabla\chi,c))$"^^La Te X ep
in defining formulation dp "$M$, Hydraulic Conductivity"^^La Te X ep
in defining formulation dp "$\chi$, Mechanical Deformation"^^La Te X ep
in defining formulation dp "$\kappa$, Fluid Intrinsic Permeability (Porous Medium)"^^La Te X ep
in defining formulation dp "$\mu$, External Chemical Potential"^^La Te X ep
in defining formulation dp "$c$, Concentration"^^La Te X ep
description ap "Boundary condition for diffusion equation"@en

Poro-Visco-Elastic Diffusion Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PoroViscoElasticDiffusionEquation

belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Free Energy Density ni
contains quantity op Hydraulic Conductivity ni
contains quantity op Mechanical Deformation ni
contains quantity op Time ni
generalizes formulation op Fick Equation ni
defining formulation dp "$\dot c(t,x) = - \nabla\cdot(M(x,\nabla\chi(t,x),c(t,x))\nabla\partial_c\Phi(x,\nabla \chi(t,x),c(t,x)))$"^^La Te X ep
in defining formulation dp "$M$, Hydraulic Conductivity"^^La Te X ep
in defining formulation dp "$\Phi$, Free Energy Density"^^La Te X ep
in defining formulation dp "$\chi$, Mechanical Deformation"^^La Te X ep
in defining formulation dp "$c$, Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
description ap "mathematical formulation for diffusion in poro-visco-elastic models"@en

Poro-Visco-Elastic Evolutionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PoroViscoElasticEvolution

This is relevant in many applications in thermo-mechanics, solid-state batteries, poroelasticity in biological tissue, hydrogen storage, and elastomeric materials.
belongs to
Research Problem c
has facts
contained in field op Continuum Mechanics ni
description ap "simulation of coupled mechanical deformation of solids to other physical processes such as heat conduction or diffusion of chemical species"@en
doi I D ap zamm.202300486 ep

Poro-Visco-Elastic Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PoroViscoElasticModel

The elastic stresses are given via the derivative of a free energy density function, the viscous stresses are of Kelvin-Voigt type and formulated in terms of a dissipation potental. The evolution of the concentration is given via a diffusion equation that is pulled-back to the reference configuration. The mobility law depends nonlinearly on the deformation gradient and the concentration itself.
belongs to
Mathematical Model c
has facts
models op Poro-Visco-Elastic Evolution ni
is deterministic dp "true"^^boolean
is space-continuous dp "true"^^boolean
is time-continuous dp "true"^^boolean
description ap "mathematical model describing the coupled evolution of the mechanical deformation and the concentration of a species"@en
doi I D ap zamm.202300486 ep

Poro-Visco-Elastic Quasistatic Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PoroViscoElasticQuasistaticEquation

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Poro-Visco-Elastic Model ni
contains quantity op Concentration ni
contains quantity op External Force Density ni
contains quantity op Free Energy Density ni
contains quantity op Hyperstress Potential ni
contains quantity op Mechanical Deformation ni
contains quantity op Spatial Variable ni
contains quantity op Time ni
contains quantity op Viscous Dissipation Potential ni
defining formulation dp "$-\nabla\cdot(\partial_{\nabla \chi} \Phi(x,\nabla\chi(t,x),c(t,x)) + \partial_{\nabla\dot\chi}\zeta(x,\nabla\dot\chi(t,x),\nabla\chi(t,x),c(t,x)) - \nabla\cdot \partial_{D^2\chi} H(x,D^2\chi(t,x)))=f(t,x)$"^^La Te X ep
in defining formulation dp "$H$, Hyperstress Potential"^^La Te X ep
in defining formulation dp "$\Phi$, Free Energy Density"^^La Te X ep
in defining formulation dp "$\chi$, Mechanical Deformation"^^La Te X ep
in defining formulation dp "$\zeta$, Viscous Dissipation Potential"^^La Te X ep
in defining formulation dp "$c$, Concentration"^^La Te X ep
in defining formulation dp "$f$, External Force Density"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$x$, Spatial Variable"^^La Te X ep
description ap "equation using linear momentum without inertia for mechanical deformation"@en

Power Setni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PowerSet

belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
description ap "mathematical set containing all subsets of a given set"@en
wikidata I D ap Q205170 ep

Pressureni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Pressure

Force applied over an area
belongs to
Quantity Kind c
has facts
qudt I D ap Pressure ep
wikidata I D ap Q39552 ep

Probability Distributionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ProbabilityDistribution

mathematical function that describes the probability of occurrence of different possible outcomes in a (real world or statistical computer) experiment
belongs to
Quantity c
has facts
description ap "statistical function that describes the likelihood of obtaining all possible values that a random variable can take"@en
alt Label ap "Probability Density"@en
wikidata I D ap Q200726 ep

Product 1 Concentrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Product1Concentration

belongs to
Quantity c
has facts
generalized by quantity op Concentration ni
description ap "amount of product 1 present in a reaction environment"@en

Product 1 Concentration ODE (Bi Bi Reaction Ordered with single central Complex)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Product1ConcentrationODEBiBiOrderedsingleCC

Ordinary differential equation describing the product 1 concentration over time in a bi bi enzymatic reaction following the ordered mechanism with a single central Complex.
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{P_1}}{dt} = k_{5} * c_{EP_1} - k_{-5} * c_{E} * c_{P_1}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{P_1}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{EP_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-5}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{5}$, Reaction Rate Constant"^^La Te X ep

Product 1 Concentration ODE (Bi Bi Reaction Ordered)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Product1ConcentrationODEBiBiOrdered

Ordinary differential equation describing the product 1 concentration over time in a bi bi enzymatic reaction following the ordered mechanism.
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{P_1}}{dt} = k_{5} * c_{EP_1} - k_{-5} * c_{E} * c_{P_1}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{P_1}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{EP_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-5}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{5}$, Reaction Rate Constant"^^La Te X ep

Product 1 Concentration ODE (Bi Bi Reaction Ping Pong)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Product1ConcentrationODEBiBiPingPong

Ordinary differential equation describing the product 1 concentration over time in a bi bi enzymatic reaction following the ping pong mechanism.
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{P_1}}{dt} = k_{2} * c_{ES_1} - k_{-2} * c_{E*} * c_{P_1}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{P_1}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{E*}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep

Product 1 Concentration ODE (Bi Bi Reaction Theorell-Chance)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Product1ConcentrationODEBiBiTheorellChance

Ordinary differential equation describing the product 1 concentration over time in a bi bi enzymatic reaction following the Theorell-Chance mechanism.
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{P_1}}{dt} = k_{2} * c_{ES_1} * c_{S_2} - k_{-2} * c_{EP_2} * c_{P_1}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{P_1}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{EP_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep

Product 2 Concentrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Product2Concentration

belongs to
Quantity c
has facts
generalized by quantity op Concentration ni
description ap "amount of product 2 present in a reaction environment"@en

Product 2 Concentration ODE (Bi Bi Reaction Ordered with single central Complex)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Product2ConcentrationODEBiBiOrderedsingleCC

Ordinary differential equation describing the product 2 concentration over time in a bi bi enzymatic reaction following the ordered mechanism with a single central Complex.
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{P_2}}{dt} = k_{4} * c_{ES_{1}S_{2}=EP_{1}P_{2}} - k_{-4} * c_{EP_1} * c_{P_2}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{P_2}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{EP_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_{1}S_{2}=EP_{1}P_{2}}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep

Product 2 Concentration ODE (Bi Bi Reaction Ordered)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Product2ConcentrationODEBiBiOrdered

Ordinary differential equation describing the product 2 concentration over time in a bi bi enzymatic reaction following the ordered mechanism.
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{P_2}}{dt} = k_{4} * c_{EP_{1}P_{2}} - k_{-4} * c_{EP_1} * c_{P_2}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{P_2}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{EP_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{EP_{1}P_{2}}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep

Product 2 Concentration ODE (Bi Bi Reaction Ping Pong)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Product2ConcentrationODEBiBiPingPong

Ordinary differential equation describing the product 2 concentration over time in a bi bi enzymatic reaction following the ping-pong mechanism.
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{P_2}}{dt} = k_{4} * c_{E*S_2} - k_{-4} * c_{P_2} * c_{E}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{P_2}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{E*S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{4}$, Reaction Rate Constant"^^La Te X ep

Product 2 Concentration ODE (Bi Bi Reaction Theorell-Chance)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Product2ConcentrationODEBiBiTheorellChance

Ordinary differential equation describing the product 2 concentration over time in a bi bi enzymatic reaction following the Theorell-Chance mechanism.
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{P_2}}{dt} = k_{3} * c_{EP_2} - k_{-3} * c_{E} * c_{P_2}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{P_2}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{EP_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_2}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep

Product Concentrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ProductConcentration

belongs to
Quantity c
has facts
generalized by quantity op Concentration ni
description ap "amount of product present in a reaction environment"@en

Product Concentration ODE (Uni Uni Reaction)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ProductConcentrationODEUniUni

ODE for change in concentraion of product in an Uni Uni reaction over time
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{P}}{dt}=k_{2}*c_{ES}-k_{-2}*c_{E}*c_{P}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{P}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{ES}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep

Proton Electron Mass Rationi back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ProtonElectronMassRatio

belongs to
Quantity Kind c
has facts
nondimensionalizes quantity op Proton Mass ni
is dimensionless dp "true"^^boolean
qudt I D ap Value Proton Electron Mass Ratio ep
wikidata I D ap Q2912520 ep

Proton Massni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ProtonMass

The mass of a proton is a fundamental physical constant, approximately equal to 1.6726219×10^−27 kilograms
belongs to
Quantity c
has facts
generalized by quantity op Mass ni
description ap "fundamental physical constant giving the proton rest mass"@en
qudt I D ap Proton Mass ep
wikidata I D ap Q97275155 ep

PTN Lineni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PTNLine

belongs to
Quantity c
has facts
description ap "single line in a public transport network (PTN)"@en
wikidata I D ap "https://www.wikidata.org/wiki/Q125209036"

Public Transportation Networkni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#PublicTransportationNetwork

We assume that it is an undirected graph.
belongs to
Mathematical Formulation c
has facts
defining formulation dp "$PTN=(V,E)$"^^La Te X ep
in defining formulation dp "$E$, edges of network"^^La Te X ep
in defining formulation dp "$V$, nodes of network"^^La Te X ep
description ap "graph given by a set of stops or stations and a set of direct connections between them"@en
wikidata I D ap Q18325841 ep

Quantum Angular Momentum Operatorni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumAngularMomentumOperator

In quantum mechanics, the angular momentum operator is one of several related operators analogous to classical angular momentum. The angular momentum operator plays a central role in the theory of atomic and molecular physics and other quantum problems involving rotational symmetry.
belongs to
Quantity c
has facts
generalized by quantity op Quantum Mechanical Operator ni
description ap "quantum mechanical operator related to rotational symmetry"@en
wikidata I D ap Q1190143 ep

Quantum Classical Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumClassicalModel

Typically used for a system comprising of light/fast and heavy/slow particles where the classical approximation can be only justified for the latter ones
belongs to
Mathematical Model c
has facts
contains formulation op Schrödinger-Newton Equation ni
contains initial condition op Initial Classical Momentum ni
contains initial condition op Initial Classical Position ni
contains initial condition op Initial Quantum State ni
contains model op Classical Dynamics Model ni
contains model op Quantum Model (Closed System) ni
is space-continuous dp "true"^^boolean
is time-continuous dp "true"^^boolean
description ap "hybrid quantum-classical model for a system with fast and slow degrees of freedom"@en

Quantum Conditional Quasi-Solvabilityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumConditionalQuasiSolvability

For certain Hamiltonians, the concept of Conditional Quasi-Solvability holds: There are exact solutions of the time-independent Schrödinger equation for a certain number of low-lying quantum states (quasi-exact solvability), if and only if certain relations of the parameters of the Hamiltonian hold (conditionally exact solvability). For examples with trigonometric and hyperbolic potentials, see the annotating DOIs.
belongs to
Computational Task c
has facts
contains formulation op Quantum Hamiltonian (Electric Dipole) ni
contains formulation op Quantum Hamiltonian (Electric Polarizability) ni
contains formulation op Quantum Hamiltonian (Linear Rotor) ni
contains formulation op Schrödinger Equation (Time Independent) ni
contains input op Rotational Constant ni
contains output op Electric Field ni
contains output op Quantum Eigen Energy ni
contains output op Quantum State Vector (Stationary) ni
description ap "exact solutions of the time-independent Schrödinger equation for a certain number of low-lying states if certain relations of the parameters hold"@en
doi I D ap 1.4864465 ep
doi I D ap Phys Rev. A.91.022111 ep
doi I D ap Phys Rev A.97.053417 ep
doi I D ap e2017 80134 6 ep
doi I D ap fphy.2014.00037 ep

Quantum Damping Rateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumDampingRate

Quantum damping rates can be used - together with quantum jump operators - to describe the dissipation and/or decoherence of the quantum dynamics in a Lindblad equation (for open quantum systems)
belongs to
Quantity c
has facts
generalized by quantity op Reaction Rate Constant ni
description ap "rate at which quantum coherence is lost in a system due to interactions with its environment"@en
alt Label ap "Dissipative Transition Rate"@en

Quantum Density Operatorni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumDensityOperator

belongs to
Quantity c
has facts
generalized by quantity op Quantum Mechanical Operator ni
generalizes quantity op Quantum State Vector ni
description ap "matrix that describes an ensemble of physical systems as quantum states"@en

Quantum Eigen Energyni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumEigenEnergy

Eigenenergy are obtained as eigenvalues of the Quantum Hamiltonian Operator by solving the time-independent Schrödinger equation.
belongs to
Quantity c
has facts
contained in formulation op Schrödinger Equation (Time Independent) ni
description ap "specific, quantized energy levels that a quantum system can possess"@en
wikidata I D ap Q190524 ep
wikidata I D ap Q230883 ep

Quantum Eigen Energy (Anharmonic)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumEigenEnergyAnharmonic

belongs to
Mathematical Formulation c
has facts
contains quantity op Anharmonicity Constant ni
contains quantity op Number of Particles ni
contains quantity op Quantum Eigen Energy ni
contains quantity op Quantum Number ni
contains quantity op Vibration Frequency (Harmonic) ni
defining formulation dp "$E_n=\sum_{r=1}^{3N-6}\omega_k\left( n_r + \frac{1}{2} \right) +\sum_{r \gt s} \chi_{rs} k\left( n_r + \frac{1}{2} \right) k\left( n_s + \frac{1}{2} \right)$"^^La Te X ep
in defining formulation dp "$E$, Quantum Eigen Energy"^^La Te X ep
in defining formulation dp "$N$, Number of Particles"^^La Te X ep
in defining formulation dp "$\chi$, Anharmonicity Constant"^^La Te X ep
in defining formulation dp "$\omega$, Vibration Frequency (Harmonic)"^^La Te X ep
in defining formulation dp "$n$, Quantum Number"^^La Te X ep
description ap "Eigenenergies of anharmonic oscillator systems, e.g. molecular vibrations, beyond the harmonic approximation"
wikidata I D ap Q545228 ep

Quantum Eigen Energy (Harmonic)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumEigenEnergyHarmonic

belongs to
Mathematical Formulation c
has facts
contains quantity op Number of Particles ni
contains quantity op Planck Constant ni
contains quantity op Quantum Eigen Energy ni
contains quantity op Quantum Number ni
contains quantity op Vibration Frequency (Harmonic) ni
generalized by formulation op Quantum Eigen Energy (Anharmonic) ni
defining formulation dp "$E_n=\sum_{k=1}^{3N-6}\left( n_k + \frac{1}{2} \right) \hbar \omega_k$"^^La Te X ep
in defining formulation dp "$E$, Quantum Eigen Energy"^^La Te X ep
in defining formulation dp "$N$, Number of Particles"^^La Te X ep
in defining formulation dp "$\hbar$, Planck Constant"^^La Te X ep
in defining formulation dp "$\omega$, Vibration Frequency (Harmonic)"^^La Te X ep
in defining formulation dp "$n$, Quantum Number"^^La Te X ep
description ap "Eigenenergies of (single or coupled, for N particles) harmonic oscillators, e.g. molecular vibrations, within the harmonic approximation"@en
wikidata I D ap Q677864 ep

Quantum Eigen Energy (Intermolecular)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumEigenEnergyIntermolecular

For simplicity, here only for a chromophore interacting with solvent molecules of a different species. Hence, only non-degenerate perturbation theory (up to 2nd order) is used here. First and second order results for the 0->1 vibrational frequency|energy shifts are given as two separate formulations.
belongs to
Mathematical Formulation c
has facts
contains formulation op Vibrational Frequency Shift (1st Order) ni
contains formulation op Vibrational Frequency Shift (2nd Order) ni
description ap "Eigenenergies of molecular vibrations, including the effects of intermolecular vibrations"@en

Quantum Hamiltonian (Electric Charge)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumHamiltonianElectricCharge

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Liouville-von Neumann Equation ni
contained as formulation in op Quantum Lindblad Equation ni
contained as formulation in op Schrödinger Equation (Time Dependent) ni
contains quantity op Electric Charge ni
contains quantity op Electric Potential ni
contains quantity op Quantum Hamiltonian Operator ni
generalizes formulation op Quantum Hamiltonian (Electric Dipole) ni
defining formulation dp "$H=H_0+q \mathcal{E}$"^^La Te X ep
in defining formulation dp "$H_0$, Quantum Hamiltonian Operator"^^La Te X ep
in defining formulation dp "$\mathcal{E}$, Electric Potential"^^La Te X ep
in defining formulation dp "$q$, Electric Charge"^^La Te X ep
description ap "quantum-mechanical Hamiltonian for a particle with an electric charge interacting with external electric fields"@en

Quantum Hamiltonian (Electric Dipole)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumHamiltonianElectricDipole

Semiclassical first order approximation
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Liouville-von Neumann Equation ni
contained as formulation in op Quantum Lindblad Equation ni
contained as formulation in op Schrödinger Equation (Time Dependent) ni
contains quantity op Electric Dipole Moment ni
contains quantity op Electric Field ni
contains quantity op Quantum Hamiltonian Operator ni
defining formulation dp "$H=H_0-\mu \cdot \mathcal{E}$"^^La Te X ep
in defining formulation dp "$H$, Quantum Hamiltonian Operator"^^La Te X ep
in defining formulation dp "$H_0$, Quantum Hamiltonian Operator (non-interacting system)"^^La Te X ep
in defining formulation dp "$\mathcal{E}$, Electric Field"^^La Te X ep
in defining formulation dp "$\mu$, Electric Dipole Moment"^^La Te X ep
description ap "Quantum-mechanical Hamiltonian for a system interacting (resonantly) through its permanent dipole moments with external electric fields"@en

Quantum Hamiltonian (Electric Polarizability)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumHamiltonianElectricPolarizability

Semiclassical second order approximation
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Liouville-von Neumann Equation ni
contained as formulation in op Quantum Lindblad Equation ni
contained as formulation in op Quantum Model (Closed System) ni
contained as formulation in op Quantum Model (Open System) ni
contained as formulation in op Schrödinger Equation (Time Dependent) ni
contained as formulation in op Schrödinger Equation (Time Independent) ni
contains quantity op Electric Field ni
contains quantity op Electric Polarizability ni
contains quantity op Quantum Hamiltonian Operator ni
defining formulation dp "$H=H_0 - \frac{1}{2} \alpha \mathcal{E}^2$"^^La Te X ep
in defining formulation dp "$H$, Quantum Hamiltonian Operator"^^La Te X ep
in defining formulation dp "$H_0$, Hamiltonian Operator (non-interacting system)"^^La Te X ep
in defining formulation dp "$\alpha$, Electric Polarizability"^^La Te X ep
in defining formulation dp "$\mathcal{E}$, Electric Field"^^La Te X ep
description ap "Quantum-mechanical Hamiltonian for a system interacting (non-resonantly) through its induced dipole moments with external electric fields"@en

Quantum Hamiltonian (Linear Rotor)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumHamiltonianLinearRotor

belongs to
Mathematical Formulation c
has facts
contains quantity op Quantum Angular Momentum Operator ni
contains quantity op Quantum Hamiltonian Operator ni
contains quantity op Quantum Number ni
contains quantity op Rotational Constant ni
generalized by formulation op Quantum Hamiltonian (Non-Rigid Rotor) ni
defining formulation dp "$E_j=Bj(j+1)$"^^La Te X ep
defining formulation dp "$\hat{H}=B\hat{J}^2$"^^La Te X ep
in defining formulation dp "$B$, Rotational Constant"^^La Te X ep
in defining formulation dp "$J$, Quantum Angular Momentum Operator"^^La Te X ep
in defining formulation dp "$\hat{H}$, Quantum Hamiltonian Operator"^^La Te X ep
in defining formulation dp "$j$, Quantum Number"^^La Te X ep
description ap "quantum-mechanical represention of a molecule as a linear rotor"@en
wikidata I D ap Q2915184 ep
wikidata I D ap Q904380 ep

Quantum Hamiltonian (Non-Rigid Rotor)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumHamiltonianNonRigidRotor

belongs to
Mathematical Formulation c
has facts
contains quantity op Centrifugal Distortion Constant ni
contains quantity op Quantum Angular Momentum Operator ni
contains quantity op Quantum Hamiltonian Operator ni
contains quantity op Quantum Number ni
contains quantity op Rotational Constant ni
defining formulation dp "$E_j=Bj(j+1)-Dj^2(j+1)^2$"^^La Te X ep
defining formulation dp "$\hat{H}=B\hat{J}^2+D\hat{J}^4$"^^La Te X ep
in defining formulation dp "$B$, Rotational Constant"^^La Te X ep
in defining formulation dp "$D$, Centrifugal Distortion Constant"^^La Te X ep
in defining formulation dp "$H$, Quantum Hamiltonian Operator"^^La Te X ep
in defining formulation dp "$J$, Quantum Angular Momentum Operator"^^La Te X ep
in defining formulation dp "$j$, Quantum Number"^^La Te X ep
description ap "quantum-mechanical represention of a molecule as a non-rigid rotor"@en
wikidata I D ap Q2915184 ep
wikidata I D ap Q904380 ep

Quantum Hamiltonian (Normal Mode)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumHamiltonianNormalMode

pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation
belongs to
Mathematical Formulation c
has facts
description ap "quantum-mechanical represention of molecular vibrations in terms of normal modes"@en
wikidata I D ap Q900488 ep

Quantum Hamiltonian (Normal Mode, Anharmonic)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumHamiltonianNormalModeAnharmonic

belongs to
Mathematical Formulation c
has facts
contains quantity op Force Constant (Anharmonic) ni
contains quantity op Normal Mode Coordinate (Dimensionless) ni
contains quantity op Normal Mode Momentum (Dimensionless) ni
contains quantity op Number of Particles ni
contains quantity op Quantum Hamiltonian Operator ni
contains quantity op Vibration Frequency (Harmonic) ni
generalized by formulation op Quantum Hamiltonian (Normal Mode) ni
defining formulation dp "$\hat{H}=\frac{1/2}\sum_{i=1}^{3N-6}\omega_i\left(\hat{p}_i^2+\hat{q}_i^2\right) + \frac{1}{6} \sum_{ijk} \phi_{ijk} q_iq_jq_k + \frac{1}{24} \sum_{ijkl} \phi_{ijk} q_iq_jq_kq_l$"^^La Te X ep
in defining formulation dp "$N$, Number of Particles"^^La Te X ep
in defining formulation dp "$\hat{H}$, Quantum Hamiltonian Operator"^^La Te X ep
in defining formulation dp "$\omega$, Vibration Frequency (Harmonic)"^^La Te X ep
in defining formulation dp "$\phi_{ijkl}$, Force Constant (Anharmonic)"^^La Te X ep
in defining formulation dp "$\phi_{ijk}$, Force Constant (Anharmonic)"^^La Te X ep
in defining formulation dp "$p$, Normal Mode Momentum (Dimensionless)"^^La Te X ep
in defining formulation dp "$q$, Normal Mode Coordinate (Dimensionless)"^^La Te X ep
description ap "quantum-mechanical represention of molecular normal modes of vibration beyond the harmonic approximation"@en

Quantum Hamiltonian (Normal Mode, Harmonic)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumHamiltonianNormalModeHarmonic

belongs to
Mathematical Formulation c
has facts
contains quantity op Normal Mode Coordinate (Dimensionless) ni
contains quantity op Normal Mode Momentum (Dimensionless) ni
contains quantity op Number of Particles ni
contains quantity op Quantum Hamiltonian Operator ni
contains quantity op Vibration Frequency (Harmonic) ni
generalized by formulation op Quantum Hamiltonian (Normal Mode, Anharmonic) ni
defining formulation dp "$\hat{H}=\frac{1/2}\sum_{i=1}^{3N-6}\omega_i\left(\hat{p}_i^2+\hat{q}_i^2\right)$"^^La Te X ep
in defining formulation dp "$N$, Number of Particles"^^La Te X ep
in defining formulation dp "$\hat{H}$, Quantum Hamiltonian Operator"^^La Te X ep
in defining formulation dp "$\omega$, Vibration Frequency (Harmonic)"^^La Te X ep
in defining formulation dp "$p$, Normal Mode Momentum (Dimensionless)"^^La Te X ep
in defining formulation dp "$q$, Normal Mode Coordinate (Dimensionless)"^^La Te X ep
description ap "quantum-mechanical represention of molecular normal modes of vibration within the harmonic approximation"@en

Quantum Hamiltonian (Normal Mode, Intermolecular)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumHamiltonianNormalModeIntermolecular

belongs to
Mathematical Formulation c
has facts
contains quantity op Force Constant (Anharmonic) ni
contains quantity op Intermolecular Potential ni
contains quantity op Normal Mode Coordinate ni
contains quantity op Normal Mode Momentum ni
contains quantity op Number of Particles ni
contains quantity op Quantum Hamiltonian Operator ni
contains quantity op Vibration Frequency (Harmonic) ni
generalizes formulation op Quantum Hamiltonian (Normal Mode, Anharmonic) ni
defining formulation dp "$\hat{H}=\frac{1}{2}\sum_{i=1}^{3N-6}\omega_i\left(\hat{p}_i^2+\hat{q}_i^2\right) + \frac{1}{6} \sum_{ijk} \phi_{ijk} q_iq_jq_k + \frac{1}{24} \sum_{ijkl} \phi_{ijk} q_iq_jq_kq_l + U(q)$"^^La Te X ep
in defining formulation dp "$N$, Number of Particles"^^La Te X ep
in defining formulation dp "$U$, Intermolecular Potential"^^La Te X ep
in defining formulation dp "$\hat{H}$, Quantum Hamiltonian Operator"^^La Te X ep
in defining formulation dp "$\omega$, Vibration Frequency (Harmonic)"^^La Te X ep
in defining formulation dp "$\phi$, Force Constant (Anharmonic)"^^La Te X ep
in defining formulation dp "$p$, Normal Mode Momentum"^^La Te X ep
in defining formulation dp "$q$, Normal Mode Coordinate"^^La Te X ep
description ap "quantum-mechanical represention of molecular normal modes of vibration, including intermolecular interaction"@en

Quantum Hamiltonian (Symmetric Top)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumHamiltonianSymmetricTop

A symmetric top is a molecule in which two moments of inertia are the same. By definition a symmetric top must have a 3-fold or higher order rotation axis. In practice, spectroscopists divide molecules into two classes of symmetric tops: Oblate symmetric tops (saucer or disc shaped), e.g., C6H6, and Prolate symmetric tops (rugby football, or cigar shaped), e.g. CH3Cl.
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Quantum Conditional Quasi-Solvability ni
contains quantity op Quantum Angular Momentum Operator ni
contains quantity op Quantum Hamiltonian Operator ni
contains quantity op Rotational Constant ni
generalizes formulation op Quantum Hamiltonian (Linear Rotor) ni
defining formulation dp "$\hat{H}=A\hat{J_A}^2 + B\hat{J_B}^2 + C\hat{J_C}^2$"^^La Te X ep
in defining formulation dp "$A$, Rotational Constant"^^La Te X ep
in defining formulation dp "$B$, Rotational Constant"^^La Te X ep
in defining formulation dp "$C$, Rotational Constant"^^La Te X ep
in defining formulation dp "$J_A$, Quantum Angular Momentum Operator"^^La Te X ep
in defining formulation dp "$J_B$, Quantum Angular Momentum Operator"^^La Te X ep
in defining formulation dp "$J_C$, Quantum Angular Momentum Operator"^^La Te X ep
in defining formulation dp "$\hat{H}$, Quantum Hamiltonian Operator"^^La Te X ep
description ap "quantum-mechanical represention of a molecule as a symmetric top"
wikidata I D ap Q904380 ep

Quantum Hamiltonian Operatorni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumHamiltonianOperator

In quantum mechanics, this is the operator representing the total energy of a quantum system, thus giving the possible outcomes of energy measurements as well as its time evolution
belongs to
Quantity c
has facts
contained in formulation op Schrödinger Equation (Time Dependent) ni
contained in formulation op Schrödinger Equation (Time Independent) ni
generalizes quantity op Classical Hamilton Function ni
description ap "operator representing the total energy of a quantum system"@en
wikidata I D ap Q660488 ep

Quantum Jump Operatorni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumJumpOperator

Quantum jump operators can be used - together with quantum damping rates - to describe the dissipation and/or decoherence of the quantum dynamics in a Lindblad equation (for open quantum systems)
belongs to
Quantity c
has facts
defined by op Quantum Jump Operator (Definition) ni
generalized by quantity op Quantum Mechanical Operator ni
description ap "mathematical concept used in the description of open quantum systems"@en
alt Label ap "Lindblad operator"@en

Quantum Jump Operator (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumJumpOperatorDefinition

belongs to
Mathematical Formulation c
has facts
contains quantity op Quantum Damping Rate ni
contains quantity op Quantum Jump Operator ni
defining formulation dp "$\hat{C_{j,k}} \equiv \sqrt{\Gamma_{k\rightarrow k}}|j\rangle\langle k|$"^^La Te X ep
in defining formulation dp "$\Gamma$, Quantum Damping Rate"^^La Te X ep
in defining formulation dp "$\hat{C}$, Quantum Jump Operator"^^La Te X ep
description ap "Together with quantum damping rates, these operators describe the dissipation and/or decoherence of open system quantum dynamics in a Lindblad equation"@en

Quantum Kinetic Operatorni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumKineticOperator

In quantum mechanics, this is the operator representing the kinetic energy of a quantum system. Typically, a function of the momenta of the particles. Hence, a derivative operator
belongs to
Quantity c
has facts
description ap "operator representing the kinetic energy of a quantum system"@en

Quantum Lindblad Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumLindbladEquation

Markovian quantum master equation for the evolution of quantum mechanical density matrices (pure or mixed states), also known as Gorini–Kossakowski–Sudarshan–Lindblad equation (GKSL equation). It generalizes the Schrödinger equation to open quantum systems; that is, systems in contacts with their surroundings. The resulting dynamics is no longer unitary, but still satisfies the property of being trace-preserving and completely positive for any initial condition
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Quantum Model (Open System) ni
contains initial condition op Initial Quantum Density ni
contains quantity op Planck Constant ni
contains quantity op Quantum Damping Rate ni
contains quantity op Quantum Density Operator ni
contains quantity op Quantum Hamiltonian Operator ni
contains quantity op Quantum Jump Operator ni
contains quantity op Time ni
generalizes formulation op Quantum Liouville Equation ni
defining formulation dp "$\frac{\mathrm d}{\mathrm{d}t}\rho=-\frac{\mathrm i}\hbar[H,\rho]+\sum _{i=1}^{N^2-1}\gamma_i\left(L_i\rho L_i^\dagger-\frac12[L_i^\dagger L_i,\rho]_+\right)$"^^La Te X ep
in defining formulation dp "$H$, Quantum Hamiltonian Operator"^^La Te X ep
in defining formulation dp "$L$, Quantum Jump Operator"^^La Te X ep
in defining formulation dp "$[\cdot,\cdot]_+$, anti-commutator"^^La Te X ep
in defining formulation dp "$\gamma > 0$, Quantum Damping Rate"^^La Te X ep
in defining formulation dp "$\hbar$, Planck Constant"^^La Te X ep
in defining formulation dp "$\rho$, Quantum Density Operator"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is time-continuous dp "true"^^boolean
description ap "describes open system quantum dynamics including dissipation and/or decoherence"@en
alt Label ap "Gorini–Kossakowski–Sudarshan–Lindblad Equation"@en
wikidata I D ap Q4476520 ep

Quantum Liouville Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumLiouvilleEquation

Just as the Schrödinger equation describes how pure states evolve in time, the von Liouville-von Neumann equation (also known as the quantum Liouville equation) describes how a density operator evolves in time. Note that there can be different density operators for pure or for mixed states.
belongs to
Mathematical Formulation c
is same as
Liouville-von Neumann Equation ni
has facts
contained as formulation in op Quantum Model (Closed System) ni
contains quantity op Planck Constant ni
contains quantity op Quantum Density Operator ni
generalizes formulation op Schrödinger Equation (Time Dependent) ni
defining formulation dp "$\frac{\mathrm d}{\mathrm{d}t}\rho(t)=-\frac{\mathrm i}\hbar[H,\rho(t)]$"^^La Te X ep
in defining formulation dp "$H$, Quantum Hamiltonian Operator"^^La Te X ep
in defining formulation dp "$\hbar$, Planck Constant"^^La Te X ep
in defining formulation dp "$\rho$, Quantum Density Operator"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is space-continuous dp "true"^^boolean
is time-continuous dp "true"^^boolean
description ap "describes how a density operator (for pure or for mixed states) evolves in time"@en
description ap "time evolution of quantum density operators; describing open system quantum dynamics"@en
alt Label ap "Liouville-von Neumann Equation"@en
wikidata I D ap Q831774 ep

Quantum Mechanical Operatorni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumMechanicalOperator

belongs to
Quantity c
has facts
generalizes quantity op Quantum Density Operator ni
generalizes quantity op Quantum Hamiltonian Operator ni
generalizes quantity op Quantum Kinetic Operator ni
generalizes quantity op Quantum Potential Operator ni
description ap "mathematical construct that corresponds to a physical observable, such as position, momentum, or energy"@en

Quantum Model (Closed System)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumModelClosedSystem

A famous example is Schrödinger's cat, but only as long as the box is not opened!
belongs to
Mathematical Model c
has facts
contains formulation op Schrödinger Equation (Time Dependent) ni
contains initial condition op Initial Quantum Density ni
contains initial condition op Initial Quantum State ni
generalizes model op Classical Dynamics Model ni
models op Molecular Reaction Dynamics ni
models op Molecular Spectroscopy (Transient) ni
is space-continuous dp "true"^^boolean
is time-continuous dp "true"^^boolean
description ap "quantum dynamics of a closed system, i.e., a system that is not interacting with its environment"

Quantum Model (Open System)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumModelOpenSystem

Quantum dynamics of an open system, i.e., a system that can exchange phase (e.g. in elastic collisions) and/or energy (e.g. in inelastic collisions) with its environment.
belongs to
Mathematical Model c
has facts
applied by task op Balanced Truncation (Bi-linear) ni
applied by task op H2 Optimal Approximation (Bi-linear) ni
contains formulation op Quantum Hamiltonian (Electric Dipole) ni
contains initial condition op Initial Quantum Density ni
generalizes model op Quantum Model (Closed System) ni
models op Molecular Reaction Dynamics ni
models op Molecular Spectroscopy (Transient) ni
is space-continuous dp "true"^^boolean
is time-continuous dp "true"^^boolean
description ap "quantum dynamics of an open system, i.e., a system that interacts with its environment"@en

Quantum Momentum Operatorni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumMomentumOperator

belongs to
Quantity c
has facts
generalized by quantity op Quantum Mechanical Operator ni
description ap "In the coordinate representation of quantum mechanics, the momentum of a particle is represented by this operator"@en
wikidata I D ap Q692457 ep

Quantum Momentum Operator (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumMomentumOperatorDefinition

belongs to
Mathematical Formulation c
has facts
contains quantity op Planck Constant ni
contains quantity op Quantum Momentum Operator ni
defines op Quantum Momentum Operator ni
defining formulation dp "$p\equiv-{\rm i}\hbar \nabla$"^^La Te X ep
in defining formulation dp "$\hbar$, Planck Constant"^^La Te X ep
in defining formulation dp "$p$, Quantum Momentum Operator"^^La Te X ep
description ap "In the coordinate representation of quantum mechanics, the momentum of a particle is represented by this operator"@en
wikidata I D ap Q692457 ep

Quantum Numberni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumNumber

In quantum physics and chemistry, quantum numbers are quantities that characterize the possible states of the system. Quantum numbers are closely related to eigenvalues of observables. When the corresponding observable commutes with the Hamiltonian, the quantum number is said to be "good", and acts as a constant of motion in the quantum dynamics.
belongs to
Quantity c
has facts
contained in formulation op Schrödinger Equation (Time Independent) ni
generalized by quantity op Integer Number (Dimensionless) ni
is dimensionless dp "true"^^boolean
description ap "quantities that characterize the possible states of the system"@en
wikidata I D ap Q232431 ep

Quantum Potential Operatorni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumPotentialOperator

In quantum mechanics, this is the operator representing the potential energy of a quantum system. Typically, a function of the positions of the particles. Hence, a multiplicative operator
belongs to
Quantity c
has facts
description ap "operator representing the potential energy of a quantum system"@en

Quantum State Vectorni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumStateVector

Abstract (Dirac) notation as a quantum state $|\psi\rangle$ or wave function $\psi(R)$ in coordinate representation
belongs to
Quantity c
has facts
contained in formulation op Schrödinger Equation (Time Dependent) ni
description ap "state of an isolated quantum system, represented as an element of a projective Hilbert space"@en
wikidata I D ap Q230883 ep

Quantum State Vector (Dynamic)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumStateVectorDynamic

Abstract (Dirac) notation as dynamic quantum states $\psi(t)>$ or wave functions $\psi(R,t)$ in coordinate representation
belongs to
Quantity c
has facts
generalized by quantity op Quantum State Vector ni
description ap "solutions of the time-dependent Schrödinger equation, giving the time evolution of a (closed) quantum system"@en

Quantum State Vector (Stationary)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantumStateVectorStationary

Abstract (Dirac) notation as stationary quantum states $\psi_n>$ or wave functions $\psi_n(R)$ in coordinate representation.
belongs to
Quantity c
has facts
generalized by quantity op Quantum State Vector ni
description ap "solutions of the time-independent Schrödinger equation, giving stationary states of a (closed) quantum system"

Radiusni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Radius

Segment in a circle or sphere from its center to its perimeter or surface and its length.
belongs to
Quantity Kind c
has facts
wikidata I D ap Q173817 ep

Rapid Equilibrium Assumptionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RapidEquilibriumAssumption

belongs to
Mathematical Formulation c
has facts
contains quantity op Reaction Rate Constant ni
defining formulation dp "$k_{catalytic} \llt k_{unbind}$"^^La Te X ep
in defining formulation dp "$k_{catalytic}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{unbind}$, Reaction Rate Constant"^^La Te X ep

Rateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Rate

Rate
belongs to
Quantity Kind c
has facts
generalizes quantity op Rate Of Aging ni
generalizes quantity op Reaction Rate ni
generalizes quantity op Risk Of Death ni
wikidata I D ap Q1144560 ep

Rate Of Agingni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RateOfAging

belongs to
Quantity c
has facts
description ap "speed at which an individual or population ages"@en

Rate Of Becoming Infectiousni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RateOfBecomingInfectious

belongs to
Quantity c
has facts
generalized by quantity op Rate ni
description ap "inverse of Incubation period"@en

Rate Of Change Of Population Density Fraction Of Exposed PDEni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RateOfChangeOfPopulationDensityFractionOfExposedPDE

Partial derivative of Population Density Fraction Of Exposed PDE w.r.t Time
belongs to
Mathematical Formulation c
has facts
contained as formulation in op PDE SEIR Model ni
contains quantity op Allee Threshold ni
contains quantity op Asymptomatic Infection Rate ni
contains quantity op Asymptomatic Recovery Rate ni
contains quantity op Diffusion Coefficient for SEIR Model ni
contains quantity op Fraction Of Population Density Of Exposed ni
contains quantity op Fraction Of Population Density Of Infectious ni
contains quantity op Fraction Of Population Density Of Susceptibles ni
contains quantity op Population Density ni
contains quantity op Rate Of Becoming Infectious ni
contains quantity op Symptomatic Infection Rate ni
contains quantity op Time ni
defining formulation dp "$\partial_t e =\operatorname{div}(D \nabla e)+\left(1-\frac{A}{n+n_0}\right) s\left(\beta_e e+\beta_i i\right)-\sigma e-\phi_e e $"^^La Te X ep
in defining formulation dp "$A$, Allee Threshold"^^La Te X ep
in defining formulation dp "$D$, Diffusion Coefficient for SEIR Model"^^La Te X ep
in defining formulation dp "$\beta_e$, Asymptomatic Infection Rate"^^La Te X ep
in defining formulation dp "$\beta_i$, Symptomatic Infection Rate"^^La Te X ep
in defining formulation dp "$\phi_e$, Asymptomatic Recovery Rate"^^La Te X ep
in defining formulation dp "$\sigma$, Rate Of Becoming Infectious"^^La Te X ep
in defining formulation dp "$e$, Fraction Of Population Density Of Exposed"^^La Te X ep
in defining formulation dp "$i$, Fraction Of Population Density Of Infectious"^^La Te X ep
in defining formulation dp "$n$, Population Density"^^La Te X ep
in defining formulation dp "$s$, Fraction Of Population Density Of Susceptibles"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is deterministic dp "true"^^boolean

Rate Of Change Of Population Density Fraction Of Infectious PDEni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RateOfChangeOfPopulationDensityFractionOfInfectiousPDE

Partial derivative of Population Density Fraction Of Infectious PDE w.r.t Time
belongs to
Mathematical Formulation c
has facts
contained as formulation in op PDE SEIR Model ni
contains quantity op Diffusion Coefficient for SEIR Model ni
contains quantity op Fraction Of Population Density Of Exposed ni
contains quantity op Fraction Of Population Density Of Infectious ni
contains quantity op Infected Recovery Rate ni
contains quantity op Rate Of Becoming Infectious ni
contains quantity op Time ni
defining formulation dp "$\partial_t i =\operatorname{div}(D \nabla i)+\sigma e-\phi_i i $"^^La Te X ep
in defining formulation dp "$D$, Diffusion Coefficient for SEIR Model"^^La Te X ep
in defining formulation dp "$\phi_i$, Infected Recovery Rate"^^La Te X ep
in defining formulation dp "$\sigma$, Rate Of Becoming Infectious"^^La Te X ep
in defining formulation dp "$e$, Fraction Of Population Density Of Exposed"^^La Te X ep
in defining formulation dp "$i$, Fraction Of Population Density Of Infectious"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is deterministic dp "true"^^boolean

Rate Of Change Of Population Density Fraction Of Removed PDEni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RateOfChangeOfPopulationDensityFractionOfRemovedPDE

Partial derivative of Population Density Fraction Of Removed PDE w.r.t Time
belongs to
Mathematical Formulation c
has facts
contained as formulation in op PDE SEIR Model ni
contains quantity op Asymptomatic Recovery Rate ni
contains quantity op Diffusion Coefficient for SEIR Model ni
contains quantity op Fraction Of Population Density Of Exposed ni
contains quantity op Fraction Of Population Density Of Infectious ni
contains quantity op Fraction Of Population Density Of Removed ni
contains quantity op Infected Recovery Rate ni
contains quantity op Time ni
defining formulation dp "$\partial_t r =\operatorname{div}(D \nabla r)+\phi_i i+\phi_e e $"^^La Te X ep
in defining formulation dp "$D$, Diffusion Coefficient for SEIR Model"^^La Te X ep
in defining formulation dp "$\phi_e$, Asymptomatic Recovery Rate"^^La Te X ep
in defining formulation dp "$\phi_i$, Infected Recovery Rate"^^La Te X ep
in defining formulation dp "$e$, Fraction Of Population Density Of Exposed"^^La Te X ep
in defining formulation dp "$i$, Fraction Of Population Density Of Infectious"^^La Te X ep
in defining formulation dp "$r$, Fraction Of Population Density Of Removed"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is deterministic dp "true"^^boolean

Rate Of Change Of Population Density Fraction Of Susceptibles PDEni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RateOfChangeOfPopulationDensityFractionOfSusceptiblesPDE

Partial derivative of Population Density Fraction Of Susceptibles PDE w.r.t Time
belongs to
Mathematical Formulation c
has facts
contained as formulation in op PDE SEIR Model ni
contains quantity op Allee Threshold ni
contains quantity op Asymptomatic Infection Rate ni
contains quantity op Diffusion Coefficient for SEIR Model ni
contains quantity op Fraction Of Population Density Of Exposed ni
contains quantity op Fraction Of Population Density Of Infectious ni
contains quantity op Fraction Of Population Density Of Susceptibles ni
contains quantity op Population Density ni
contains quantity op Symptomatic Infection Rate ni
contains quantity op Time ni
defining formulation dp "$\partial_t s =\operatorname{div}(D \nabla s)-\left(1-\frac{A}{n+n_0}\right) s\left(\beta_e e+\beta_i i\right)$"^^La Te X ep
in defining formulation dp "$A$, Allee Threshold"^^La Te X ep
in defining formulation dp "$D$, Diffusion Coefficient for SEIR Model"^^La Te X ep
in defining formulation dp "$\beta_e$, Asymptomatic Infection Rate"^^La Te X ep
in defining formulation dp "$\beta_i$, Symptomatic Infection Rate"^^La Te X ep
in defining formulation dp "$e$, Fraction Of Population Density Of Exposed"^^La Te X ep
in defining formulation dp "$i$, Fraction Of Population Density Of Infectious"^^La Te X ep
in defining formulation dp "$n$, Population Density"^^La Te X ep
in defining formulation dp "$s$, Fraction Of Population Density Of Susceptibles"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is deterministic dp "true"^^boolean

Rate Of Change Of Susceptible Citiesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RateOfChangeOfSusceptibleCities

belongs to
Quantity c
has facts
generalized by quantity op Rate ni
is dimensionless dp "true"^^boolean
description ap "rate of change of susceptible cities"@en

Rate Of Switching Influencersni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RateOfSwitchingInfluencers

Rate at which an Individual switches the Influencer they are following at a given time. Takes the opinion of the individual and the given time as inputs. Subscript represents the medium followed by the Individual.
belongs to
Quantity c
has facts
generalized by quantity op Rate ni
description ap "Rate at which an individual switches the influencer they are following at a given time"@en

Rate Of Switching Influencers Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RateOfSwitchingInfluencersFormulation

Each individual i can at any time t switch its current influencer l′ to another influencer l with a given rate. By setting the pair function to $\psi(x) = exp(−x)$, an individual has an exponentially higher rate to switch to an influencer that has a similar opinion than to an influencer with a very different opinion. This rate of switching influencers is defined by this formulation.
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Opinion Model With Influencers And Media ni
contains quantity op Link Recommendation Function ni
contains quantity op Medium Influencer Fraction ni
contains quantity op Opinion ni
contains quantity op Pair Function ni
contains quantity op Rate Of Switching Influencers ni
contains quantity op Scaling Parameter For Switching Influencers ni
contains quantity op Time ni
defining formulation dp "$\Lambda_m^{\rightarrow l}(x, t)=\eta \psi\left(\left\|z_l-x\right\|\right) r\left(\frac{n_{m, l}(t)}{\sum_{m^{\prime}=1}^M n_{m^{\prime}, l}(t)}\right)$"^^La Te X ep
in defining formulation dp "$\Lambda_m^{\rightarrow l}(x, t)$, Rate Of Switching Influencers"^^La Te X ep
in defining formulation dp "$\eta$, Scaling Parameter For Switching Influencers"^^La Te X ep
in defining formulation dp "$\psi$, Pair Function"^^La Te X ep
in defining formulation dp "$n_{m, l}$, Medium Influencer Fraction"^^La Te X ep
in defining formulation dp "$r$, Link Recommendation Function"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$x$, Opinion"^^La Te X ep
is space-continuous dp "true"^^boolean

Reaction Rateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ReactionRate

belongs to
Quantity c
has facts
description ap "speed at which a chemical reaction proceeds"@en
wikidata I D ap Q3394849 ep

Reaction Rate Constantni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RateConstant

belongs to
Quantity c
has facts
description ap "quantifies the rate of a chemical reaction"@en
wikidata I D ap Q658700 ep

Reaction Rate of Enzymeni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ReactionRateOfEnzyme

belongs to
Quantity c
has facts
generalized by quantity op Reaction Rate ni
description ap "speed at which an enzyme converts a substrate into a product"@en
wikidata I D ap Q3394849 ep

Reaction Rate of Enzyme - Product 1 - Product 2 Complexni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ReactionRateOfEnzymeProduct1Product2Complex

belongs to
Quantity c
has facts
generalized by quantity op Reaction Rate ni
wikidata I D ap Q3394849 ep

Reaction Rate of Enzyme - Product 1 Complexni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ReactionRateOfEnzymeProduct1Complex

belongs to
Quantity c
has facts
generalized by quantity op Reaction Rate ni
wikidata I D ap Q3394849 ep

Reaction Rate of Enzyme - Product 2 Complexni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ReactionRateOfEnzymeProduct2Complex

belongs to
Quantity c
has facts
generalized by quantity op Reaction Rate ni
wikidata I D ap Q3394849 ep

Reaction Rate of Enzyme - Substrate 1 - Substrate 2 = Enzyme - Product 1 - Product 2 Complexni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ReactionRateofEnzymeSubstrate1Substrate2EnzymeProduct1Product2Complex

belongs to
Quantity c
has facts
wikidata I D ap Q3394849 ep

Reaction Rate of Enzyme - Substrate 1 - Substrate 2 Complexni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ReactionRateOfEnzymeSubstrate1Substrate2Complex

belongs to
Quantity c
has facts
generalized by quantity op Reaction Rate ni
wikidata I D ap Q3394849 ep

Reaction Rate of Enzyme - Substrate 1 Complexni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ReactionRateOfEnzymeSubstrate1Complex

belongs to
Quantity c
has facts
generalized by quantity op Reaction Rate ni
wikidata I D ap Q3394849 ep

Reaction Rate of Intermediateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ReactionRateOfIntermediate

belongs to
Quantity c
has facts
generalized by quantity op Reaction Rate ni
wikidata I D ap Q3394849 ep

Reaction Rate of Intermediate - Substrate 2 Complexni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ReactionRateOfIntermediateSubstrate2Complex

belongs to
Quantity c
has facts
wikidata I D ap Q3394849 ep

Reaction Rate of Product 1ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ReactionRateOfProduct1

belongs to
Quantity c
has facts
generalized by quantity op Reaction Rate ni
wikidata I D ap Q3394849 ep

Reaction Rate of Product 2ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ReactionRateOfProduct2

belongs to
Quantity c
has facts
generalized by quantity op Reaction Rate ni
wikidata I D ap Q3394849 ep

Reaction Rate of Substrate 1ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ReactionRateOfSubstrate1

belongs to
Quantity c
has facts
generalized by quantity op Reaction Rate ni
wikidata I D ap Q3394849 ep

Reaction Rate of Substrate 2ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ReactionRateOfSubstrate2

belongs to
Quantity c
has facts
generalized by quantity op Reaction Rate ni
wikidata I D ap Q3394849 ep

Real Number (Dimensionless)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RealDimensionless

Quantity along a continuous line
belongs to
Quantity Kind c
has facts
is dimensionless dp "true"^^boolean
wikidata I D ap Q12916 ep

Reciprocal Latticeni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ReciprocalLattice

In solid state physics, the reciprocal lattice emerges from the Fourier transform of the direct lattice which is a periodic function in physical space, such as a crystal system (usually a Bravais lattice). The reciprocal lattice exists in the mathematical space of spatial frequencies, known as reciprocal space or k space, which refers to the wavevector.
belongs to
Quantity c
has facts
contained in formulation op Darwin-Howie-Whelan Equation for an unstrained crystal ni
contained in formulation op Darwin-Howie-Whelan Equation for a strained crystal ni
contained in formulation op Initial Value For Electron Scattering ni
description ap "mathematical construct to describe the diffraction patterns of crystals"@en
wikidata I D ap Q164129 ep

Reciprocal Lattice Vectorsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ReciprocalLatticeVectors

In solid state physics, the reciprocal lattice emerges from the Fourier transform of the direct lattice which is a periodic function in physical space, such as a crystal system (usually a Bravais lattice). The reciprocal lattice exists in the mathematical space of spatial frequencies, known as reciprocal space or k space, which refers to the wavevector.
belongs to
Quantity c
has facts
contained in formulation op Darwin-Howie-Whelan Equation for an unstrained crystal ni
contained in formulation op Darwin-Howie-Whelan Equation for a strained crystal ni
contained in formulation op Initial Value For Electron Scattering ni
description ap "mathematical constructs used in the study of periodic structures"@en
wikidata I D ap Q164129 ep

Recombination Of Electron Hole Pairsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RecombinationOfElectronHolePairs

For use in semiconductor physics; strictly speaking, the combined effect of recombination and generation of electron-hole pairs
belongs to
Quantity c
has facts
generalized by quantity op Reaction Rate Constant ni
description ap "the combined effect of recombination and generation of electron-hole pairs"@en

Recovery Rateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RecoveryRate

Subscript e refers to recovery rate of the Exposed class. Subscript i refers to recovery rate of of the Infectious class
belongs to
Quantity c

Recurrent Neural Network Surrogate for Discrete Element Methodni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Recurrent_Neural_Network_Surrogate_for_Discrete_Element_Method

belongs to
Mathematical Model c
has facts
models op Efficient Numerical Simulation of Soil-Tool Interaction ni
studied in op Jahnke (2022) Efficient Numerical Simulation of Soil-Tool Interaction ni

Regionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Region

belongs to
Quantity c
has facts
description ap "area of land that shares common features, which can be either natural or artificial"@en
wikidata I D ap Q82794 ep

Region Connectivityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RegionConnectivity

belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
description ap "connectivity between regions m and n / n and m / m and m"@en

Relative Removal Rateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RelativeRemovalRate

Probability that one infective will be removed from the infection process during a unit time interval. subscript i denotes the ith subpopulation. if no i is provided, then it is a single-population model.
belongs to
Quantity c
has facts
generalized by quantity op Rate ni
is dimensionless dp "true"^^boolean
description ap "probability that one infective will be removed from the infection process during a unit time interval"@en

Relativistic Momentumni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RelativisticMomentum

belongs to
Quantity c
has facts
defined by op Relativistic Momentum (Definition) ni
generalized by quantity op Momentum ni
description ap "momentum of a particle in special relativity"@en

Relativistic Momentum (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RelativisticMomentumDefinition

belongs to
Mathematical Formulation c
has facts
contains quantity op Classical Velocity ni
contains quantity op Mass ni
contains quantity op Relativistic Momentum ni
contains quantity op Speed Of Light ni
defining formulation dp "$p\equiv\frac{mv}{\sqrt{1-\frac{v^2}{c^2}}}$"^^La Te X ep
in defining formulation dp "$c$, Speed Of Light"^^La Te X ep
in defining formulation dp "$m$, Mass"^^La Te X ep
in defining formulation dp "$p$, Relativistic Momemtum"^^La Te X ep
in defining formulation dp "$v$, Classical Velocity"^^La Te X ep
description ap "momentum of a particle in special relativity"@en

Removedni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Removed

belongs to
Quantity c
has facts
generalized by op Integer Number (Dimensionless) ni
is dimensionless dp "true"^^boolean
description ap "general quantity for removed entities"@en
alt Label ap "Recovered"@en
alt Label ap "Resistant"@en

Removed At Time Step n+1 in The Multi-Population Discrete Susceptible Infectious Removed Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RemovedAtTimeStepInTheMultiPopulationSIRModel

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Multi-Population Discrete Susceptible Infectious Removed Model ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Relative Removal Rate ni
contains quantity op Number Of Removed Individuals ni
contains quantity op Time Step ni
defining formulation dp "$R_{n+1}^i = R_n^i + \gamma_i \Delta t I_n^i$"^^La Te X ep
in defining formulation dp "$I_n^i$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$R_n^i$, Number Of Removed Individuals"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Removed At Time Step n+1 in The SIR Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RemovedAtTimeStepInTheSIRModel

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Discrete Susceptible Infectious Removed Model ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Relative Removal Rate ni
contains quantity op Number Of Removed Individuals ni
contains quantity op Time Step ni
discretizes op Continuous Rate of Change of Removed in the SIR Model ni
defining formulation dp "$R_{n+1} = R_n + \gamma \Delta t I_n$"^^La Te X ep
in defining formulation dp "$I_n$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$R_n$, Number Of Removed Individuals"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Removed At Time Step n+1 in the SIR Model with Births and Deathsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RemovedAtTimeStepInTheSIRModelWithBirthsAndDeaths

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Susceptible Infectious Removed Model with Births and Deaths ni
contains quantity op Birth Rate ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Relative Removal Rate ni
contains quantity op Number Of Removed Individuals ni
contains quantity op Time Step ni
defining formulation dp "$R_{n+1} = R_n(1 - \beta \Delta t) + \gamma \Delta t I_n$"^^La Te X ep
in defining formulation dp "$I_n$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$R_n$, Number Of Removed Individuals"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\beta$, Birth Rate"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Risk Of Deathni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RiskOfDeath

belongs to
Quantity c
has facts
description ap "risk (or hazard) of death, at a certain age"@en
qudt I D ap Incidence Rate ep

Roman Archaeologyni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RomanArchaeology

belongs to
Research Field c
has facts
generalized by field op Archaeology ni
description ap "archaeological sub-discipline"@en
wikidata I D ap Q44097629 ep

Romanization Parameter Estimationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RomanizationParameterEstimation

belongs to
Computational Task c
has facts
applies model op Susceptible Infectious Epidemic Spreading Model ni
contains constraint condition op Contact Network Constraint ni
contains constraint condition op Spreading Rate (Time-dependent) Constraint ni
contains formulation op Loss Function Minimization ni
contains input op Spreading Curve (Approximate) ni
contains input op Romanized Cities Vector ni
contains output op Contact Network (Time-dependent) ni
description ap "given a set of data points the contact network and time-dependent spreading rate are determined"@en

Romanization Spreading in Northern Tunesiani back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RomanizationSpreadingInNorthernTunesia

Understanding the mechanisms and dynamics of Romanization spreading in Northern Tunisia from 146 BC to 350 AD based on sparse and fragmented archaeological data.
belongs to
Research Problem c
has facts
contained in field op Roman Archaeology ni
description ap "understanding the mechanisms and dynamics of Romanization spreading in Northern Tunisia"@en

Romanization Time Evolutionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RomanizationTimeEvolution

belongs to
Computational Task c
has facts
applies model op Susceptible Infectious Epidemic Spreading Model ni
contains formulation op Susceptible Infectious Epidemic Spreading ODE System ni
contains input op Number Of Susceptible Cities ni
contains output op Spreading Curve (Approximate) ni
contains output op Number Of Susceptible Cities ni
contains parameter op Contact Network ni
contains parameter op Spreading Rate (Time-dependent) ni
description ap "given a set of initially infected cities, a contact network, and a time-dependent spreading rate, the spreading curve for the romanization is calculated"@en

Romanized Cities Vectorni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RomanizedCitiesVector

observed number of romanized cities in the mth region at the ith time point in the $N_R$ regions
belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
description ap "observed number of romanized cities"@en

Rotational Constantni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RotationalConstant

In rotational spectroscopy, the energy levels of a molecule are often given in terms of its rotational constant
belongs to
Quantity c
has facts
description ap "defines the scale of rotational energies in molecular spectroscopy"@en
wikidata I D ap Q904380 ep

Runge–Kutta Methodni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#RungeKuttaMethod

These methods, which include the Euler method, were developed around 1900 by the German mathematicians Carl Runge and Wilhelm Kutta.
belongs to
Mathematical Formulation c
has facts
generalizes formulation op Euler Backward Method ni
generalizes formulation op Euler Forward Method ni
defining formulation dp "$\begin{array}{c|cccc} c_1 & a_{11} & a_{12}& \dots & a_{1s}\\c_2 & a_{21} & a_{22}& \dots & a_{2s}\\ \vdots & \vdots & \vdots& \ddots& \vdots\\c_s & a_{s1} & a_{s2}& \dots & a_{ss} \\\hline & b_1 & b_2 & \dots & b_s\\ \end{array}$"^^La Te X ep
description ap "family of implicit and explicit methods used in temporal discretization for the approximate solutions of differential equations"@en
wikidata I D ap Q725944 ep

Scaling Parameter For Switching Influencersni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ScalingParameterForSwitchingInfluencers

scaling parameter used in the Rate of Switching Influcners. Real number greater than 0.
belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
description ap "scaling parameter used in the rate of switching influcners"@en

Scharfetter-Gummel Schemeni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ScharfetterGummelScheme

The Scharfetter-Gummel finite volume disretization scheme is the standard numerical method for solving the van Roosbroeck system describing the semi-classical transport of free electrons and holes in a self-consistent electric field using a drift-diffusion approximation.
belongs to
Mathematical Model c
has facts
discretizes model op van Roosbroeck Model ni
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean
is space-continuous dp "false"^^boolean
description ap "finite volume disretization scheme for solving the van Roosbroeck system describing the semi-classical transport of free electrons and holes"@en
wikidata I D ap Q119844 ep
wikidata I D ap Q29367424 ep

Schrödinger Equation (Chebychev Polynomial)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SchrödingerEquationChebychevPolynomial

belongs to
Mathematical Formulation c
has facts
discretizes formulation op Schrödinger Equation (Time Dependent) ni
is time-continuous dp "false"^^boolean
description ap "Chebchev polynomial scheme for numerical integration of the time-dependent Schrödinger equation"@en
doi I D ap 0021 9991(91)90137 A ep
doi I D ap 1.448136 ep

Schrödinger Equation (Differencing Scheme)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SchrödingerEquationDifferencingScheme

belongs to
Mathematical Formulation c
has facts
contains formulation op Euler Backward Method ni
contains formulation op Euler Forward Method ni
discretizes formulation op Schrödinger Equation (Time Dependent) ni
generalizes formulation op Schrödinger Equation (Second Order Differencing) ni
is time-continuous dp "false"^^boolean
description ap "Differencing scheme (symmetric combination of Euler forward and backward in time) for numerical integration of the time-dependent Schrödinger equation"@en

Schrödinger Equation (Lie-Trotter)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SchrödingerEquationLieTrotter

First order (Lie-Trotter) split operator scheme for numerical integration of the time-dependent Schrödinger equation
belongs to
Mathematical Formulation c
has facts
contains quantity op Planck Constant ni
contains quantity op Quantum Kinetic Operator ni
contains quantity op Quantum Potential Operator ni
contains quantity op Quantum State Vector (Dynamic) ni
contains quantity op Time Step ni
discretizes formulation op Schrödinger Equation (Time Dependent) ni
generalized by formulation op Schrödinger Equation (Split Operator) ni
defining formulation dp "$|\psi(t+\Delta t)\rangle=\exp(-i\Delta t\hat{T}/ \hbar)\exp(-i\Delta t\hat{V}/ \hbar)|\psi(t)\rangle + \mathcal{O}(\Delta t)$"^^La Te X ep
in defining formulation dp "$T$, Quantum Kinetic Operator"^^La Te X ep
in defining formulation dp "$V$, Quantum Potential Operator"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\hbar$, Planck constant"^^La Te X ep
in defining formulation dp "$\psi$, Quantum State Vector (Dynamic)"^^La Te X ep
is time-continuous dp "false"^^boolean
doi I D ap 0021 9991(82)90091 2 ep
doi I D ap 0021 9991(91)90137 A ep
doi I D ap 1.444501 ep

Schrödinger Equation (Second Order Differencing)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SchrödingerEquationSecondOrderDifferencing

Essentially a symmetric (and symplectic!) combination of Euler forward and backward methods
belongs to
Mathematical Formulation c
has facts
contains formulation op Euler Backward Method ni
contains formulation op Euler Forward Method ni
contains quantity op Planck Constant ni
contains quantity op Quantum Hamiltonian Operator ni
contains quantity op Quantum State Vector (Dynamic) ni
contains quantity op Time Step ni
discretizes formulation op Schrödinger Equation (Time Dependent) ni
defining formulation dp "$|\psi(t+\Delta t)\rangle = |\psi(t-\Delta t)\rangle -2i\Delta t \hat{H}/\hbar |\psi(t)\rangle + \mathcal{O}(\Delta t)^3$"^^La Te X ep
in defining formulation dp "$H$, Quantum Hamiltonian Operator"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\hbar$, Planck constant"^^La Te X ep
in defining formulation dp "$\psi$, Quantum State Vector (Dynamic)"^^La Te X ep
is time-continuous dp "false"^^boolean
description ap "Second order differencing scheme for numerical integration of the time-dependent Schrödinger equation"@en
doi I D ap 0021 9991(91)90137 A ep
doi I D ap 1.436072 ep

Schrödinger Equation (Split Operator)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SchrödingerEquationSplitOperator

belongs to
Mathematical Formulation c
has facts
discretizes formulation op Schrödinger Equation (Time Dependent) ni
is time-continuous dp "false"^^boolean
description ap "Split operator scheme for numerical integration of the time-dependent Schrödinger equation"@en

Schrödinger Equation (Strang-Marchuk)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SchrödingerEquationStrangMarchuk

belongs to
Mathematical Formulation c
has facts
contains quantity op Planck Constant ni
contains quantity op Quantum Kinetic Operator ni
contains quantity op Quantum Potential Operator ni
contains quantity op Quantum State Vector (Dynamic) ni
contains quantity op Time Step ni
discretizes formulation op Schrödinger Equation (Time Dependent) ni
generalized by formulation op Schrödinger Equation (Split Operator) ni
defining formulation dp "$|\psi(t+\Delta t)\rangle=\exp(-i\Delta t\hat{T}/ (2\hbar))\exp(-i\Delta t\hat{V}/ \hbar)\exp(-i\Delta t\hat{T}/ (2\hbar))|\psi(t)\rangle + \mathcal{O}(\Delta t)^2$"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\hat{T}$, Quantum Kinetic Operator"^^La Te X ep
in defining formulation dp "$\hat{V}$, Quantum Potential Operator"^^La Te X ep
in defining formulation dp "$\hbar$, Planck constant"^^La Te X ep
in defining formulation dp "$\psi(t)$, Quantum State Vector (Dynamic)"^^La Te X ep
is time-continuous dp "false"^^boolean
description ap "Second order (Strang-Marchuk) split operator scheme for numerical integration of the time-dependent Schrödinger equation"@en
doi I D ap 0021 9991(82)90091 2 ep
doi I D ap 0021 9991(91)90137 A ep
doi I D ap 1.444501 ep
wikidata I D ap Q25303744 ep

Schrödinger Equation (Time Dependent)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SchroedingerEquationTimeDependent

One of the fundamental postulates of Quantum Mechanics on the time evolution of quantum states.
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Quantum Model (Closed System) ni
contains quantity op Planck Constant ni
contains quantity op Quantum Hamiltonian Operator ni
contains quantity op Quantum State Vector (Dynamic) ni
contains quantity op Time ni
generalizes formulation op Classical Hamilton Equations ni
defining formulation dp "$\mathrm{i} \hbar \frac{\partial}{\partial t} | \psi (t) \rangle = \hat{H} | \psi (t) \rangle$"^^La Te X ep
in defining formulation dp "$H$, Quantum Hamiltonian Operator"^^La Te X ep
in defining formulation dp "$\hbar$, Planck Constant"^^La Te X ep
in defining formulation dp "$\psi(t)$, Quantum State Vector (Dynamic)"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is space-continuous dp "true"^^boolean
is time-continuous dp "true"^^boolean
description ap "partial differential equation describing how the quantum state of a non-relativistic physical system changes with time"@en
wikidata I D ap Q165498 ep

Schrödinger Equation (Time Independent)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SchrödingerEquationTimeIndependent

belongs to
Mathematical Formulation c
has facts
contains quantity op Quantum Eigen Energy ni
contains quantity op Quantum Hamiltonian Operator ni
contains quantity op Quantum Number ni
contains quantity op Quantum State Vector (Stationary) ni
generalized by formulation op Schrödinger Equation (Time Dependent) ni
generalizes formulation op Darwin-Howie-Whelan Equation for a strained crystal ni
defining formulation dp "$\hat H | \psi_n \rangle = E_n | \psi_n \rangle$"^^La Te X ep
in defining formulation dp "$E_n$, Quantum Eigen Energy"^^La Te X ep
in defining formulation dp "$H$, Quantum Hamiltonian Operator"^^La Te X ep
in defining formulation dp "$\psi_n$, Quantum State Vector (Stationary)"^^La Te X ep
in defining formulation dp "$n$, Quantum Number"^^La Te X ep
description ap "eigenvalue equation for the quantum-mechanical Hamiltonian operator, yielding stationary states (wave functions), along with their corresponding energies"@en
wikidata I D ap Q25829357 ep

Schrödinger-Newton Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SchroedingerNewtonEquation

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Quantum Classical Model ni
contains formulation op Classical Newton Equation ni
contains formulation op Schrödinger Equation (Time Dependent) ni
is space-continuous dp "true"^^boolean
is time-continuous dp "true"^^boolean
description ap "Coupled equations describing the time evolution in (hybrid) quantum-classical dynamics"@en

Second Condition For Positive Solutions In The Multi Population SIS Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SecondConditionForPositiveSolutionsInTheMultiPopulationSIS_Model

belongs to
Mathematical Formulation c
has facts
contained as constraint condition in op Multi-Population Discrete Susceptible Infectious Susceptible Model ni
contains formulation op Between Population Contact Rate Equation ni
contains quantity op Between Population Contact Rate ni
contains quantity op Relative Removal Rate ni
contains quantity op Time Step ni
defining formulation dp "$\alpha_{ii} \Delta t \leq (\sqrt{1 - a_i} + \sqrt{ \gamma_i \Delta t})^2$"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\gamma_i$, Relative Removal Rate"^^La Te X ep
in defining formulation dp "$a_i$, Between Population Contact Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Second Condition For Positive Solutions In The SIR Model with Births and Deathsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SecondConditionForPositiveSolutionsInTheSIRModelWithBirthsAndDeaths

belongs to
Mathematical Formulation c
has facts
contained as constraint condition in op Susceptible Infectious Removed Model with Births and Deaths ni
contains quantity op Birth Rate ni
contains quantity op Contact Rate ni
contains quantity op Time Step ni
defining formulation dp "$\alpha \Delta t \leq ( 1 + \sqrt{ \beta \Delta t})^2$"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha$, Contact Rate"^^La Te X ep
in defining formulation dp "$\beta$, Birth Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Second Condition For Positive Solutions In The SIS Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SecondConditionForPositiveSolutionsInTheSISModel

belongs to
Mathematical Formulation c
has facts
contained as constraint condition in op Discrete Susceptible Infectious Susceptible Model ni
contains quantity op Contact Rate ni
contains quantity op Relative Removal Rate ni
contains quantity op Time Step ni
defining formulation dp "$\alpha \Delta t < ( 1 + \sqrt{ \gamma \Delta t})^2$"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha$, Contact Rate"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Second Condition For Positive Solutions In The SIS Model with Births and Deathsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SecondConditionForPositiveSolutionsInTheSISModelWithBirthsAndDeaths

belongs to
Mathematical Formulation c
has facts
contained as constraint condition in op Susceptible Infectious Susceptible Model with Births and Deaths ni
contains quantity op Birth Rate ni
contains quantity op Contact Rate ni
contains quantity op Relative Removal Rate ni
contains quantity op Time Step ni
defining formulation dp "$\alpha \Delta t < ( 1 + \sqrt{ (\beta + \gamma) \Delta t})^2$"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha$, Contact Rate"^^La Te X ep
in defining formulation dp "$\beta$, Birth Rate"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Second Eigenvalue of Orthogonal Matrixni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SecondEigenvalueofOrthogonalMatrix

belongs to
Quantity c
has facts
description ap "second eigenvalue of an orthogonal matrix"@en

SEIR Derivative Relationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SEIRDerivativerelation

belongs to
Mathematical Formulation c
has facts
contained as formulation in op SEIR Derivative Relation ni
contains quantity op Fraction Of Population Density Of Exposed ni
contains quantity op Fraction Of Population Density Of Infectious ni
contains quantity op Fraction Of Population Density Of Removed ni
contains quantity op Fraction Of Population Density Of Susceptibles ni
defining formulation dp "$\nu^T D \nabla s =\nu^T D \nabla e=\nu^T D \nabla i=\nu^T D \nabla r=0 $"^^La Te X ep
in defining formulation dp "$D$, 'Diffusion Coefficient for SEIR Model'"^^La Te X ep
in defining formulation dp "$e$, Fraction Of Population Density Of Exposed"^^La Te X ep
in defining formulation dp "$i$, Fraction Of Population Density Of Infectious"^^La Te X ep
in defining formulation dp "$r$, Fraction Of Population Density Of Removed"^^La Te X ep
in defining formulation dp "$s$, Fraction Of Population Density Of Susceptibles"^^La Te X ep
in defining formulation dp "$v$, Unit Outer Normal To Domain"^^La Te X ep

Semiconductor Charge Neutralityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SemiconductorChargeNeutrality

The physical concept of local charge neutrality in semiconductor is characterized by the absence of space charge regions. Hence, the Poisson equation for the electric field potential simplifies to the Laplace equation.
belongs to
Computational Task c
has facts
applies model op Drift-Diffusion Model ni
applies model op Electron Shuttling Model ni
contains constant op Permittivity (Vacuum) ni
contains formulation op Dirichlet Boundary Condition For Electric Potential ni
contains formulation op Laplace Equation For The Electric Potential ni
contains formulation op Neumann Boundary Condition For Electric Potential ni
contains formulation op Periodic Boundary Condition For Electric Potential ni
contains input op Applied External Voltage ni
contains input op Electrode Interfaces ni
contains input op Permittivity (Dielectric) ni
contains output op Electric Potential ni
generalized by task op Semiconductor Thermal Equilibrium ni
description ap "concept of local charge neutrality in semiconductor"@en

Semiconductor Current Voltageni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SemiconductorCurrentVoltage

In simulations of semiconductor devices, one is usually interested in IV-curves displaying the current voltage charateristics, i.e., the dependence of terminal currents on applied voltages. Therefore, calculating terminal currents accurately is crucial to a successful postprocessing of the simulated field data.
belongs to
Computational Task c
has facts
applies model op Drift-Diffusion Model ni
contains constant op Permittivity (Vacuum) ni
description ap "calculating IV-curves displaying the current voltage charateristics of a semiconductor device"@en

Semiconductor Physicsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SemiconductorPhysics

belongs to
Research Field c
has facts
contains problem op Current flow in semiconductor devices ni
description ap "study of semiconductor materials and devices"@en
wikidata I D ap Q4483523 ep

Semiconductor Thermal Equilibriumni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SemiconductorThermalEquilibrium

The goal is to enforce that the drift-diffusion model (aka van Roosbroeck model) of a semiconductor is consistent with the thermodynamic equilibrium, which is a physical state defined by vanishing currents:
belongs to
Computational Task c
has facts
applies model op Drift-Diffusion Model ni
contains constant op Permittivity (Vacuum) ni
description ap "enforce that the drift-diffusion model of a semiconductor is consistent with the thermodynamic equilibrium"@en

Sensitivity Analysis of Complex Kinetic Systemsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SensitivityAnalysisOfComplexKineticSystems

Study of uncertainty in Complex Kinetic Systems
belongs to
Computational Task c
has facts
wikidata I D ap Q1889114 ep

Sensory Organni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Sensory_Organ

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Sensory Organ Model ni
contains quantity op Fiber Contraction Velocity ni
contains quantity op Fiber Stretch ni
contains quantity op Muscle Spindle Firing Rate ni
defining formulation dp "$$I_\text{spindle} = \sum^{N_\text{spindle}}_{j=1} w_jIa_j\left(\lambda^{j}_{\text{f}}, \dot{\lambda}^{j}_{\text{f}}\right)$$"^^La Te X ep
in defining formulation dp "$Ia_j$, Muscle Spindle Firing Rate"^^La Te X ep
in defining formulation dp "$N$, Amount of spindles"^^La Te X ep
in defining formulation dp "$\dot{\lambda}_{\text{f}}$, Fibre Contraction Velocity"^^La Te X ep
in defining formulation dp "$\lambda_{\text{f}}$, Fibre Stretch"^^La Te X ep
description ap "representing a sensory organ"@en

Sensory Organ Currentni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SensoryOrganCurrent

belongs to
Quantity c
has facts
generalized by quantity op Electric Current ni
description ap "sensory organ current"@en

Sensory Organ Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Sensory_Organ_Model

belongs to
Mathematical Model c
has facts
studied in op Homs-Pons (2024) Coupled simulations and parameter inversion for neural system and electrophysiological muscle models ni
is deterministic dp "true"^^boolean
is linear dp "true"^^boolean
is space-continuous dp "true"^^boolean
is time-continuous dp "true"^^boolean
description ap "mathematical model to detect macroscopic length change in the muscels and provide the motor neurons with this information."@en
doi I D ap gamm.202370009 ep

Simulation of Complex Kinetic Systemsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SimulationOfComplexKineticSystems

belongs to
Computational Task c
has facts
description ap "study of the time-dependent behavior of complex kinetic systems"@en

Simulation of TEM Imagesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SimulationOfTEMImages

belongs to
Computational Task c
has facts
applies model op Dynamical Electron Scattering Model ni
description ap "simulating TEM (transmission electron microscopy) images by means of the Darwin Howie Whelan equation"@en
doi I D ap s11082 020 02356 y ep
doi I D ap rspa.2022.0317 ep

Slyke (1914) The mode of action of urease and of enzymes in generalni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Slyke_1914_The_mode_of_action_of_urease_and_of_enzymes_in_general

belongs to
Publication c
has facts
invents op Uni Uni Reaction (Michaelis Menten Model without Product - Irreversibility Assumption) ni
doi I D ap S0021 9258(18)88300 4 ep

Solar System Equations Of Motionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SolarSystemEquationsOfMotion

The acceleration of a celestial body can be calculated from Newton's Law of Gravitation. Each body attracts each other body, the total acceleration being the sum of all these attractions.
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Solar System Model ni
contains quantity op Classical Acceleration ni
contains quantity op Classical Position ni
contains quantity op Gravitational Constant ni
contains quantity op Mass ni
defining formulation dp "$\vec{a}_j = \sum_{i \neq j}^n G \frac{M_i}{|\vec{r}_i - \vec{r}_j|^3} (\vec{r}_i - \vec{r}_j)$"^^La Te X ep
in defining formulation dp "$G$, Gravitational Constant"^^La Te X ep
in defining formulation dp "$a$, Classical Acceleration"^^La Te X ep
in defining formulation dp "$m$, Mass"^^La Te X ep
in defining formulation dp "$r$, Classical Position"^^La Te X ep
description ap "mathematical formulation describing the motion of the planets around the sun"@en
wikidata I D ap Q7069658 ep

Solar System Mechanicsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SolarSystemMechanics

belongs to
Research Problem c
has facts
contained in field op Celestial Mechanics ni
description ap "study of the motion of the planets within our solar system"@en
wikidata I D ap Q184274 ep

Solar System Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SolarSystemModel

Neglecting dwarf planets, satellites (e.g. Moon), asteroids, as well as the interaction with other stars or exoplanets. The numerical model of the Solar System consists of a set of mathematical equations, which, when solved, give the approximate positions of the planets as a function of time.
belongs to
Mathematical Model c
has facts
models op Solar System Mechanics ni
description ap "classical mechanics model of the sun (fixed) and the 8 planets (moving) as point masses"@en
wikidata I D ap Q7069658 ep

Sort ancient Egyptian Objectsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SortAncientEgyptianObjects

belongs to
Research Problem c
has facts
contained in field op Egyptology ni
modeled by op Object Comparison Model ni

Spatial Variableni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SpatialVariable

belongs to
Quantity c
has facts
description ap "variable that describes a spatial dimension"@en

Species Transportni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SpeciesTransport

belongs to
Research Problem c
has facts
contained in field op Continuum Mechanics ni
modeled by op Diffusion Model ni
description ap "transport of chemical species in some substance"@en

Speed Of Lightni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SpeedOfLight

belongs to
Quantity c
has facts
generalized by quantity op Velocity ni
description ap "speed of electromagnetic waves in vacuum"@en
qudt I D ap Speed Of Light Vacuum ep
wikidata I D ap Q2111 ep

Speed Of Light (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SpeedOfLightDefinition

belongs to
Mathematical Formulation c
has facts
contains quantity op Permeability (Vacuum) ni
contains quantity op Permittivity (Vacuum) ni
contains quantity op Speed Of Light ni
defines op Speed Of Light ni
defining formulation dp "$c \equiv \frac{1}{\sqrt{\epsilon_0 \mu_0}}$"^^La Te X ep
in defining formulation dp "$\epsilon_0$, Permittivity (Vacuum)"^^La Te X ep
in defining formulation dp "$\mu_0$, Permeability (Vacuum)"^^La Te X ep
in defining formulation dp "$c$, Speed Of Light"^^La Te X ep
description ap "speed of electromagnetic waves in vacuum"@en

Spherical Harmonics Expansion (3D)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SphericalHarmonicsExpansion3D

belongs to
Mathematical Formulation c
has facts
contains quantity op Azimuthal Angle ni
contains quantity op Polar Angle ni
contains quantity op Radius ni
defining formulation dp "$V(r,\theta,\varphi) = \sum_{\ell=0}^\infty\, \sum_{m=-\ell}^\ell C^m_\ell(r)\, Y^m_\ell(\theta,\varphi)$"^^La Te X ep
in defining formulation dp "$\theta$, Azimuthal Angle"^^La Te X ep
in defining formulation dp "$\theta$, Polar Angle"^^La Te X ep
in defining formulation dp "$r$, Radius"^^La Te X ep
description ap "Representing a function in 3D in terms of spherical harmonics with distance(radius)-dependent coefficients"@en

Spin Qbit Shuttlingni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SpinQbitShuttling

Spin-qubit shuttles are novel functional elements in modular architectures of semiconductor quantum processors, that have the capability of solving the scalability problem. Such coherent quantum links serve to interconnect different processor units and enable the transfer of quantum information over longer distances across the chip by physical transport of electrons.
belongs to
Research Problem c
has facts
contained in field op Electromagnetism ni
contained in field op Semiconductor Physics ni
description ap "novel functional elements in modular architectures of semiconductor quantum processors"@en
doi I D ap W I A S. P R E P R I N T.3082 ep

Spreading Curve (Approximate)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ApproximateSpreadingCurve

belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
description ap "approximate spreading curve through time"@en

Spreading Curve (Approximate, Formulation)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ApproximateSpreadingCurveFormulation

Definition of approximate spreading curve through time.
belongs to
Mathematical Formulation c
has facts
contains initial condition op Initial Number Of Infected Cities ni
contains quantity op Spreading Curve (Approximate) ni
contains quantity op Number of Cities ni
contains quantity op Number of Regions ni
contains quantity op Rate Of Change Of Susceptible Cities ni
contains quantity op Time ni
contains quantity op Contact Network (Time-dependent) ni
defining formulation dp "$\phi (t\, |\,\sigma , i(0)) \equiv \left( P_m - \int _{0}^t \left. \frac{ds_m(\tau )}{d\tau } \right| _{\sigma , P_m - i(0)} d\tau \right) _{m = 1,\ldots ,N_R}$"^^La Te X ep
in defining formulation dp "$N_R$, Number of Regions"^^La Te X ep
in defining formulation dp "$P_m$, Number of Cities"^^La Te X ep
in defining formulation dp "$\frac{ds_m(\tau)}{d\tau}$, Rate of Change of susceptible Cities"^^La Te X ep
in defining formulation dp "$\phi$, Spreading Curve (Approximate)"^^La Te X ep
in defining formulation dp "$\sigma$, Contact Network (Time-dependent)"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is dimensionless dp "true"^^boolean
is dynamic dp "true"^^boolean

Spreading of Infectious Diseasesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SpreadingOfInfectiousDiseases

belongs to
Research Problem c
has facts
contained in field op Epidemiology ni

Spreading Rate (Time-dependent)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SpreadingRateTimeDependent

belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
description ap "spreading rate at time t"@en

Spreading Rate (Time-dependent) Constraintni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SpreadingRateTimeDependentConstraint

constraints applying to time-dependent spreading rate
belongs to
Mathematical Formulation c
has facts
contains quantity op Spreading Rate (Time-dependent) ni
defining formulation dp "$\forall \, t \ge 0,\, 0 \le \alpha (t) < \infty$"^^La Te X ep
in defining formulation dp "$\alpha$, Spreading Rate (Time-dependent)"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean
is dynamic dp "false"^^boolean

Spring Constantni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SpringConstant

The spring constant is the constant of proportionality in Hooke’s law
belongs to
Quantity c
is same as
Force Constant (Harmonic) ni
has facts
description ap "constant of proportionality in Hooke’s law"@en
wikidata I D ap Q338261 ep

Stability Autonomous Systemni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#StabilityAutonomousSystem

The asymptotic stability of fixed points of a system of constant coefficient linear differential equations of first order (aka linear autonomious system, time-invariant system, $\dot{x}=Ax$) can be analyzed using the eigenvalues of the corresponding matrix.
belongs to
Mathematical Formulation c
has facts
contained as assumption in op Lyapunov Equation Controllability ni
contained as assumption in op Lyapunov Equation Observability ni
contained as assumption in op Lyapunov Generalized Controllability ni
contained as assumption in op Lyapunov Generalized Observability ni
contains quantity op Control System Matrix A ni
defining formulation dp "$\Re(eig(A))$"^^La Te X ep
in defining formulation dp "$A$, Control System Matrix A"^^La Te X ep
description ap "asymptotic stability of fixed points of a system of constant coefficient linear differential equations of first order"@en
wikidata I D ap Q1756677 ep

Statisticsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Statistics

belongs to
Research Field c
has facts
description ap "study of the collection, analysis, interpretation, and presentation of data"@en
mardi I D ap Item: Q57236 ep
wikidata I D ap Q12483 ep

Steady State Assumptionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SteadyStateAssumption

belongs to
Mathematical Formulation c
has facts
contains quantity op Complexed Enzyme Concentration ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{EX}}{dt} = 0$"^^La Te X ep
in defining formulation dp "$c_{EX}$, Complexed Enzyme Concentration"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
description ap "rate of bound enzyme formation and breakdown is equal"@en

Stokes Darcy Coupling Conditionsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#StokesDarcyCouplingConditions

belongs to
Mathematical Formulation c
has facts
contains formulation op Beavers–Joseph-Saffman Condition ni
contains formulation op Continuity of the Normal Mass Flux ni
contains formulation op Continuity of the Normal Stresses ni
description ap "Coupling free flow of an incompressible fluid (Stokes) to a flow in/through a permeable media (Darcy)"@en

Stokes Darcy Equation (Discretized, pv)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#StokesDarcyEquationDiscretizedPV

Equation (9) from the referenced 2021 arXiv manuscript by Schmalfuss et al.: Discrete model of Stokes-Darcy as a pressure-velocity (pv) formulation, to be solved for every time step
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Stokes Darcy Model (Discretized) ni
contains quantity op Fluid Pressure (Free Flow) ni
contains quantity op Fluid Pressure (Porous Medium) ni
contains quantity op Fluid Velocity (Free Flow) ni
defining formulation dp "$\begin{pmatrix} \begin{bmatrix} V & B \\ C & 0 \end{bmatrix} & \begin{bmatrix} B'_1 \\ 0 \end{bmatrix} \\ \begin{bmatrix} C'_1 & 0\end{bmatrix} & D' \end{pmatrix} \begin{pmatrix} \begin{bmatrix} v^{ff} \\ p^{ff} \end{bmatrix} \\ p^{pm} \end{pmatrix} = \begin{pmatrix} \begin{bmatrix} g \\ 0 \end{bmatrix} \\ 0 \end{pmatrix}$"^^La Te X ep
in defining formulation dp "$p^{ff}$, Fluid Pressure (Free Flow)"^^La Te X ep
in defining formulation dp "$p^{pm}$, Fluid Pressure (Porous Medium)"^^La Te X ep
in defining formulation dp "$v^{ff}$, Fluid Velocity (Free Flow)"^^La Te X ep
is space-continuous dp "false"^^boolean
description ap "discrete model of Stokes-Darcy as a pressure-velocity (pv) formulation"@en
doi I D ap ar Xiv.2108.13229 ep

Stokes Darcy Equation (Discretized, td)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#StokesDarcyEquationDiscretizedTD

Equation (8) from the referenced 2021 arXiv manuscript by Schmalfuss et al.: Discrete model of Stokes-Darcy as a two-domain (td) formulation, to be solved for every time step
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Stokes Darcy Model (Discretized) ni
contains quantity op Fluid Pressure (Porous Medium) ni
defining formulation dp "$\begin{pmatrix} A' & B' \\ C' & D'\end{pmatrix} \begin{pmatrix} x^{ff} \\ p^{pm} \end{pmatrix} = \begin{pmatrix} b^{ff} \\ 0 \end{pmatrix}$"^^La Te X ep
in defining formulation dp "$p^{pm}$, Fluid Pressure (Porous Medium)"^^La Te X ep
is space-continuous dp "false"^^boolean
description ap "discrete model of Stokes-Darcy as a two-domain (td) formulation"@en
doi I D ap ar Xiv.2108.13229 ep

Stokes Darcy Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#StokesDarcyModel

belongs to
Mathematical Model c
has facts
contains coupling condition op Stokes Darcy Coupling Conditions ni
contains model op Darcy Model ni
contains model op Stokes Model ni
models op Free flow coupled to porous media flow ni
description ap "free flow model of an incompressible fluid (Stokes model) coupled to a flow in/through a permeable media (Darcy equation)"@en
doi I D ap ar Xiv.2108.13229 ep

Stokes Darcy Model (Discretized)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#StokesDarcyModelDiscretized

belongs to
Mathematical Model c
has facts
contains model op Darcy Model (Discretized) ni
contains model op Stokes Model (Discretized) ni
discretizes model op Stokes Darcy Model ni
description ap "discretized version of a Stokes Darcy model for the incompressible flow in/through porous media"@en
doi I D ap j.camwa.2020.02.012 ep

Stokes Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#StokesEquation

Stokes equation (also Stokes flow, Stokes law, creeping flow or creeping motion) describes a fluid flow with small advective inertial forces compared to viscous forces, with a low Reynolds number ($Re << 1$). It occurs in situations with very slow fluid velocities, high viscosities, or small flow length scales.
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Stokes Model ni
contains quantity op Fluid Density ni
contains quantity op Fluid Kinematic Viscosity (Free Flow) ni
contains quantity op Fluid Pressure (Free Flow) ni
contains quantity op Fluid Velocity (Free Flow) ni
contains quantity op Time ni
defining formulation dp "$\begin{align} \frac{\partial v}{\partial t} + \nabla \cdot ( - \nu \left(\nabla v^{ff} + \nabla v^{\mathrm{ff,T}} \right)+ \rho^{-1} p^{ff} I ) &= 0 \\ \nabla \cdot v^{ff} &= 0 \end{align}$"^^La Te X ep
in defining formulation dp "$I$, Identity Map"^^La Te X ep
in defining formulation dp "$\nu$, Fluid Kinematic Viscosity (Free Flow)"^^La Te X ep
in defining formulation dp "$\rho$, Fluid Density"^^La Te X ep
in defining formulation dp "$p^{ff}$, Fluid Pressure (Free Flow)"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
in defining formulation dp "$v^{ff}$, Fluid Velocity (Free Flow)"^^La Te X ep
is space-continuous dp "true"^^boolean
is time-continuous dp "true"^^boolean
description ap "describes a fluid flow with small advective inertial forces compared to viscous forces"@en

Stokes Equation (Euler Backward)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#StokesEquationEulerBackward

Discretizing the Stokes equation by a first-oder backward Euler scheme in time
belongs to
Mathematical Formulation c
has facts
discretizes formulation op Stokes Equation ni
is time-continuous dp "false"^^boolean
description ap "discretizing the Stokes equation by a first-oder backward Euler scheme in time"@en

Stokes Equation (Finite Volume)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#StokesEquationFiniteVolume

Discretizing the Stokes equation by a finite volume scheme in space
belongs to
Mathematical Formulation c
has facts
discretizes formulation op Stokes Equation ni
is space-continuous dp "false"^^boolean
description ap "discretizing the Stokes equation by a finite volume scheme in space"@en

Stokes Model (Discretized)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#StokesModelDiscretized

belongs to
Mathematical Model c
has facts
contains formulation op Stokes Equation (Euler Backward) ni
contains formulation op Stokes Equation (Finite Volume) ni
discretizes model op Stokes Model ni
description ap "discretized version of a Stokes model for a fluid flow with small advective inertial forces compared to viscous forces"@en

Stress Free Muscle Lengthni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#StressFreeMuscleLength

belongs to
Quantity c
has facts
generalized by quantity op Length ni
description ap "length at which a muscle generates minimal or no passive tension"@en

Stress Free Tendon Lengthni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#StressFreeTendonLength

belongs to
Quantity c
has facts
generalized by quantity op Length ni
description ap "length of a tendon when it is not under any tension or stress"@en

Stress Of Crystalni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#StressOfCrystal

belongs to
Quantity c
has facts
description ap "stress of a crystal used in theory of elasticity"@en

Stress Tensor (Cauchy)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#StressTensorCauchy

In the case of finite deformations, the Cauchy stress tensors express the stress relative to the present configuration. This is in contrast to the Piola–Kirchhoff stress tensor which expresses the stress relative to the reference configuration. For infinitesimal deformations and rotations, the Cauchy and Piola–Kirchhoff tensors are identical.
belongs to
Quantity c
has facts
generalized by quantity op Mechanical Stress ni
similar to quantity op Stress Tensor (Piola-Kirchhoff) ni
description ap "stress relative to the present configuration"@en
wikidata I D ap Q13409892 ep

Stress Tensor (Piola-Kirchhoff)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#StressTensorPiolaKirchhoff

In the case of finite deformations, the Piola–Kirchhoff stress tensors express the stress relative to the reference configuration. This is in contrast to the Cauchy stress tensor which expresses the stress relative to the present configuration. For infinitesimal deformations and rotations, the Cauchy and Piola–Kirchhoff tensors are identical.
belongs to
Quantity c
has facts
generalized by quantity op Mechanical Stress ni
description ap "stress relative to the reference configuration"@en
wikidata I D ap Q9291589 ep

Suan (2010) Kinetic and reactor modelling of lipases catalyzed (R,S)-1-phenylethanol resolutionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Suan_2010_Kinetic_and_reactor_modelling_of_lipases_catalyzed_R_S-1-phenylethanol_resolution

Lee Suan, Chua and Kian Kai, Cheng and Chew Tin, Lee and Sarmid, Mohamad Roji (2010) Kinetic and reactor modelling of lipases catalyzed (R,S)-1-phenylethanol resolution. Iranica Journal of Energy and Environment, 1 (3). pp. 234-245. ISSN 2079-2115
belongs to
Publication c
has facts
surveys op Bi Bi Reaction Ping Pong Mechanism (ODE Model) ni

Subcellular DAE Systemni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Subcellular_DAE_System

A differential-algebraic equation systems that describes the muscle stress generation an a microscopic scale by means of internal state variables and describes the activation of the ion channels.
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Subcellular Model ni
contains quantity op Ion Current ni
contains quantity op Time ni
contains quantity op Transmembrane Potential ni
defining formulation dp "$\begin{align} \frac{\partial\mathbf{y}}{\partial t} &= G \left(\mathbf{y}, V^{\text{f}}_{\text{m}} \right) \\ I_{\text{ion}} &= I_{\text{ion}} \left(V^{\text{f}}_{\text{m}}, \mathbf{y}\right) \end{align}$"^^La Te X ep
in defining formulation dp "$I_{\text{ion}}$, Ion current"^^La Te X ep
in defining formulation dp "$V^{\text{f}}_{\text{m}}$, Transmembrane potential"^^La Te X ep
in defining formulation dp "$\mathbf{y}$, Vector of internal state variables"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
description ap "differential-algebraic equation systems that describes the muscle stress generation"@en

Subcellular Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Subcellular_Model

Determines the lumped activation parameter and models the activation of ion channels in response to changes in the muscle fibers transmembrane.
belongs to
Mathematical Model c
has facts
studied in op Homs-Pons (2024) Coupled simulations and parameter inversion for neural system and electrophysiological muscle models ni
is deterministic dp "true"^^boolean
is dynamic dp "true"^^boolean
is space-continuous dp "true"^^boolean
is time-continuous dp "true"^^boolean
description ap "determines the lumped activation parameter and models the activation of ion channels"@en
doi I D ap gamm.202370009 ep

Substrate 1 Concentrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Substrate1Concentration

belongs to
Quantity c
has facts
generalized by quantity op Concentration ni
description ap "amount of substrate 1 present in a reaction environment"@en

Substrate 1 Concentration ODE (Bi Bi Reaction Ordered with single central Complex)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Substrate1ConcentrationODEBiBiOrderedsingleCC

Ordinary differential equation describing the substrate 1 concentration over time in a bi bi enzymatic reaction following the ordered mechanism with a single central Complex
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
similar to formulation op Substrate 1 Concentration ODE (Bi Bi Reaction Ordered) ni
defining formulation dp "$\frac{dc_{S_1}}{dt} = k_{-1} * c_{ES_1} - k_{1} * c_{E} * c_{S_1}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{S_1}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep

Substrate 1 Concentration ODE (Bi Bi Reaction Ordered)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Substrate1ConcentrationODEBiBiOrdered

Ordinary differential equation describing the substrate 1 concentration over time in a bi bi enzymatic reaction following the ordered mechanism.
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{S_1}}{dt} = k_{-1} * c_{ES_1} - k_{1} * c_{E} * c_{S_1}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{S_1}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep

Substrate 1 Concentration ODE (Bi Bi Reaction Ping Pong)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Substrate1ConcentrationODEBiBiPingPong

Ordinary differential equation describing the substrate 1 concentration over time in a bi bi enzymatic reaction following the ping pong mechanism.
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{S_1}}{dt} = k_{-1} * c_{ES_1} - k_{1} * c_{E} * c_{S_1}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{S_1}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep

Substrate 1 Concentration ODE (Bi Bi Reaction Theorell-Chance)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Substrate1ConcentrationODEBiBiTheorellChance

Ordinary differential equation describing the substrate 1 concentration over time in a bi bi enzymatic reaction following the Theorell-Chance mechanism.
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{S_1}}{dt} = k_{-1} * c_{ES_1} - k_{1} * c_{E} * c_{S_1}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{S_1}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_1}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep

Substrate 2 Concentrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Substrate2Concentration

belongs to
Quantity c
has facts
generalized by quantity op Concentration ni
description ap "amount of substrate 2 present in a reaction environment"@en

Substrate 2 Concentration ODE (Bi Bi Reaction Ordered with single central Complex)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Substrate2ConcentrationODEBiBiOrderedsingleCC

Ordinary differential equation describing the substrate 2 concentration over time in a bi bi enzymatic reaction following the ordered mechanism with a single central Complex.
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{S_2}}{dt} = k_{-2} * c_{ES_{1}S_{2}=EP_{1}P_{2}} - k_{2} * c_{ES_1} * c_{S_2}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{S_2}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_{1}S_{2}=EP_{1}P_{2}}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep

Substrate 2 Concentration ODE (Bi Bi Reaction Ordered)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Substrate2ConcentrationODEBiBiOrdered

Ordinary differential equation describing the substrate 2 concentration over time in a bi bi enzymatic reaction following the ordered mechanism.
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{S_2}}{dt} = k_{-2} * c_{ES_{1}S_{2}} - k_{2} * c_{ES_1} * c_{S_2}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{S_2}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_{1}S_{2}}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep

Substrate 2 Concentration ODE (Bi Bi Reaction Ping Pong)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Substrate2ConcentrationODEBiBiPingPong

Ordinary differential equation describing the substrate 2 concentration over time in a bi bi enzymatic reaction following the ping pong mechanism.
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{S_2}}{dt} = k_{-3} * c_{E*S_2} - k_{3} * c_{E*} * c_{S_2}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{S_2}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{E*S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E*}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-3}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{3}$, Reaction Rate Constant"^^La Te X ep

Substrate 2 Concentration ODE (Bi Bi Reaction Theorell-Chance)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Substrate2ConcentrationODEBiBiTheorellChance

Ordinary differential equation describing the substrate 2 concentration over time in a bi bi enzymatic reaction following the Theorell-Chance mechanism.
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{S_2}}{dt} = k_{-2} * c_{EP_2} * c_{P_1} - k_{2} * c_{ES_1} * c_{S_2}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{S_2}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{EP_2}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{ES_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P_1}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S_2}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep

Substrate Concentrationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SubstrateConcentration

belongs to
Quantity c
has facts
generalized by quantity op Concentration ni
is dimensionless dp "false"^^boolean
description ap "amount of substrate present in a reaction environment"@en

Substrate Concentration ODE (Uni Uni Reaction)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SubstrateConcentrationODEUniUni

ODE describing a change in Substrate concentration in an Uni Uni reaction over time
belongs to
Mathematical Formulation c
has facts
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\frac{dc_{S}}{dt}=-k_{1}*c_{E}*c_{S}+k_{-1}*c_{ES}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{S}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{ES}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep

Surface Force Densityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SurfaceForceDensity

belongs to
Quantity c
has facts
description ap "concept that describes the force per unit area acting on a surface"@en

Susceptible Cities ODEni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SusceptibleCitiesODE

ordinary differential equation describing the rate of change of susceptible cities
belongs to
Mathematical Formulation c
has facts
contains quantity op Contact Network ni
contains quantity op Number Of Infected Cities ni
contains quantity op Number of Regions ni
contains quantity op Number Of Susceptible Cities ni
contains quantity op Rate Of Change Of Susceptible Cities ni
contains quantity op Spreading Rate (Time-dependent) ni
contains quantity op Time ni
defining formulation dp "$\frac{ds_m(t)}{dt} &= -s_m(t) * \alpha(t) \sum_{n=1}^{N_R} G_{m,n} * i_n(t)$"^^La Te X ep
in defining formulation dp "$G_{m,n}$, Contact Network"^^La Te X ep
in defining formulation dp "$N_R$, Number of Regions"^^La Te X ep
in defining formulation dp "$\alpha(t)$, Spreading Rate (Time-dependent)"^^La Te X ep
in defining formulation dp "$\frac{ds_m(t)}{dt}$, Rate Of Change Of Susceptible Cities"^^La Te X ep
in defining formulation dp "$i_n(t)$, Number Of Infected Cities"^^La Te X ep
in defining formulation dp "$s_m(t)$, Number Of Susceptible Cities"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean
is dynamic dp "true"^^boolean
is linear dp "false"^^boolean

Susceptible Infectious Epidemic Spreading Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SusceptibleInfectiousEpidemicSpreadingModel

belongs to
Mathematical Model c
has facts
contains formulation op Susceptible Infectious Epidemic Spreading ODE System ni
contains initial condition op Initial Number Of Infected Cities ni
models op Romanization Spreading in Northern Tunesia ni
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean
is dynamic dp "true"^^boolean
description ap "model for the susceptible infectious epidemic spreading on a network with time-dependent spreading rate."@en

Susceptible Infectious Epidemic Spreading ODE Systemni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SusceptibleInfectiousEpidemicSpreadingODESystem

Formulations describing the spreading in a susceptible infectious epidemic model on a network with time-dependent spreading rate.
belongs to
Mathematical Formulation c
has facts
contains formulation op Conservation of City Numbers ni
contains formulation op Susceptible Cities ODE ni
contains quantity op Contact Network ni
contains quantity op Number of Cities ni
contains quantity op Number Of Infected Cities ni
contains quantity op Number of Regions ni
contains quantity op Number Of Susceptible Cities ni
contains quantity op Rate Of Change Of Susceptible Cities ni
contains quantity op Region ni
contains quantity op Spreading Rate (Time-dependent) ni
contains quantity op Time ni
defining formulation dp "$\begin{align*} \frac{ds_m(t)}{dt} &= -s_m(t) * \alpha(t) \sum_{n=1}^{N_R} G_{m,n} * i_n(t) \\ i_m(t) &= P_m - s_m(t) \end{align*}$"^^La Te X ep
in defining formulation dp "$G_{m,n}$, Contact Network"^^La Te X ep
in defining formulation dp "$N_R$, Number of Regions"^^La Te X ep
in defining formulation dp "$P_m$, Number of Cities"^^La Te X ep
in defining formulation dp "$\alpha(t)$, Spreading Rate (Time-dependent)"^^La Te X ep
in defining formulation dp "$\frac{ds_m(t)}{dt}$, Rate of Change of Susceptible Cities"^^La Te X ep
in defining formulation dp "$i$, Number Of Infected Cities"^^La Te X ep
in defining formulation dp "$m$, Region"^^La Te X ep
in defining formulation dp "$n$, Region"^^La Te X ep
in defining formulation dp "$s_m(t)$, Number Of Susceptible Cities"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean
is dynamic dp "true"^^boolean
is linear dp "false"^^boolean

Susceptible Infectious Removed Model with Births and Deathsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SusceptibleInfectiousRemovedModelWithBirthsAndDeaths

belongs to
Mathematical Model c
has facts
models op Spreading of Infectious Diseases ni
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean
description ap "discrete-time SIR model with births and deaths"@en

Susceptible Infectious Susceptible Model with Births and Deathsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SusceptibleInfectiousSusceptibleModelWithBirthsAndDeaths

belongs to
Mathematical Model c
has facts
models op Spreading of Infectious Diseases ni
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean
description ap "discrete-time SIS model with births and deaths"@en

Susceptiblesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Susceptibles

belongs to
Quantity c
has facts
generalized by op Integer Number (Dimensionless) ni
generalizes op Number Of Susceptible Cities ni
generalizes op Number Of Susceptible Individuals ni
is dimensionless dp "true"^^boolean
description ap "general quantity for susceptible entities"@en

Susceptibles At Time Step n +1 in the Multi Population SI Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SusceptiblesAtTimeStepInTheMultiPopulationSIModel

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Multi-Population Discrete Susceptible Infectious Model ni
contains quantity op Contact Rate Between Two Groups ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time Step ni
contains quantity op Total Population Size ni
defining formulation dp "$S_{n+1}^i = S_n^i \left(1- \sum_{k=1}^{K} \frac{\alpha_{ik} \Delta t}{N^i} I_n^k\right)$"^^La Te X ep
in defining formulation dp "$I_n^i$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N^i$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_n^i$, Number Of Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha_{ik}$, Contact Rate Between Two Groups"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Susceptibles At Time Step n +1 in the Multi Population SIR Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SusceptiblesAtTimeStepInTheMultiPopulationSIRModel

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Multi-Population Discrete Susceptible Infectious Removed Model ni
contains quantity op Contact Rate Between Two Groups ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Relative Removal Rate ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time Step ni
contains quantity op Total Population Size ni
defining formulation dp "$S_{n+1}^i = S_n^i\left(1-\sum_{k=1}^K\frac{\alpha_{ik} \Delta t}{N^i} I_n^k\right)$"^^La Te X ep
in defining formulation dp "$I_n^i$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N^i$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_n^i$, Number Of Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha_{ik}$, Contact Rate Between Two Groups"^^La Te X ep
in defining formulation dp "$\gamma_i$, Relative Removal Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Susceptibles At Time Step n +1 in the Multi Population SIS Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SusceptiblesAtTimeStepInTheMultiPopulationSISModel

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Multi-Population Discrete Susceptible Infectious Susceptible Model ni
contains quantity op Contact Rate Between Two Groups ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Relative Removal Rate ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time Step ni
contains quantity op Total Population Size ni
defining formulation dp "$S_{n+1}^i = S_n^i \left(1- \sum_{k=1}^K \frac{\alpha_{ik} \Delta t}{N^i} I_n^k\right) + \gamma_i \Delta t I_n^i$"^^La Te X ep
in defining formulation dp "$I_n^i$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N^i$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_n^i$, Number Of Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha_{ik}$, Contact Rate Between Two Groups"^^La Te X ep
in defining formulation dp "$\gamma_i$, Relative Removal Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Susceptibles At Time Step n+1 in The SI Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SusceptiblesAtTimeStepInTheSIModel

equation to define S at time step (n+1) in the SI Model
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Discrete Susceptible Infectious Model ni
contains quantity op Contact Rate ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time Step ni
contains quantity op Total Population Size ni
defining formulation dp "$S_{n+1}=S_n\left(1-\frac{\alpha \Delta t}{N} I_n\right)$"^^La Te X ep
in defining formulation dp "$/alpha$, Contact Rate"^^La Te X ep
in defining formulation dp "$I_n$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_n$, Number Of Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Susceptibles At Time Step n+1 in The SIR Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SusceptiblesAtTimeStepInTheSIRModel

equation to define S at time step (n+1) in the SIR Model
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Discrete Susceptible Infectious Removed Model ni
contains quantity op Contact Rate ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time Step ni
contains quantity op Total Population Size ni
discretizes op Continuous Rate of change of Susceptibles in the SIR Model ni
defining formulation dp "$S_{n+1}=S_n\left(1-\frac{\alpha \Delta t}{N} I_n\right)$"^^La Te X ep
in defining formulation dp "$I_n$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_n$, Number Of Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha$, Contact Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Susceptibles At Time Step n+1 in the SIR Model with births and deathsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SusceptiblesAtTimeStepInTheSIRModelWithBirthsAndDeaths

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Susceptible Infectious Removed Model with Births and Deaths ni
contains quantity op Birth Rate ni
contains quantity op Contact Rate ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time Step ni
contains quantity op Total Population Size ni
defining formulation dp "$S_{n+1}=S_n\left(1-\frac{\alpha \Delta t}{N} I_n + \beta \Delta t (N - S_n)\right)$"^^La Te X ep
in defining formulation dp "$I_n$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_n$, Number Of Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha$, Contact Rate"^^La Te X ep
in defining formulation dp "$\beta$, Birth Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Susceptibles At Time Step n+1 in The SIS Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SusceptiblesAtTimeStepInTheSISModel

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Discrete Susceptible Infectious Susceptible Model ni
contains quantity op Contact Rate ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Relative Removal Rate ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time Step ni
contains quantity op Total Population Size ni
defining formulation dp "$S_{n+1}=S_n\left(1-\frac{\alpha \Delta t}{N} I_n\right) + \gamma \Delta t I_n$"^^La Te X ep
in defining formulation dp "$I_n$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_n$, Number Of Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha$, Contact Rate"^^La Te X ep
in defining formulation dp "$\gama$, Relative Removal Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Susceptibles At Time Step n+1 in The SIS Model with births and deathsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SusceptiblesAtTimeStepInTheSISModelWithBirthsAndDEaths

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Susceptible Infectious Susceptible Model with Births and Deaths ni
contains quantity op Birth Rate ni
contains quantity op Contact Rate ni
contains quantity op Number Of Infectious Individuals ni
contains quantity op Relative Removal Rate ni
contains quantity op Number Of Susceptible Individuals ni
contains quantity op Time Step ni
contains quantity op Total Population Size ni
defining formulation dp "$S_{n+1}=S_n\left(1-\frac{\alpha \Delta t}{N} I_n\right) + \gamma \Delta t I_n + \beta \Delta t (N - S_n)$"^^La Te X ep
in defining formulation dp "$I_n$, Number Of Infectious Individuals"^^La Te X ep
in defining formulation dp "$N$, Total Population Size"^^La Te X ep
in defining formulation dp "$S_n$, Number Of Susceptible Individuals"^^La Te X ep
in defining formulation dp "$\Delta t$, Time Step"^^La Te X ep
in defining formulation dp "$\alpha$, Contact Rate"^^La Te X ep
in defining formulation dp "$\beta$, Birth Rate"^^La Te X ep
in defining formulation dp "$\gamma$, Relative Removal Rate"^^La Te X ep
is deterministic dp "true"^^boolean
is time-continuous dp "false"^^boolean

Sylvester (1884) Sur léquations en matrices px = xqni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Sylvester_1884_Sur_léquations_en_matrices_px_xq

belongs to
Publication c

Sylvester Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SylvesterEquation

Due to the different sizes of A, B, C, the matrix X will be rectangular in general
belongs to
Mathematical Formulation c
has facts
contained as formulation in op H2 Optimal Approximation ni
contains quantity op Unknown Matrix ni
generalizes formulation op Lyapunov Equation ni
generalizes formulation op Sylvester Equation Controllability ni
generalizes formulation op Sylvester Equation Observability ni
invented in op Sylvester (1884) Sur léquations en matrices px = xq ni
defining formulation dp "$AX+XB=C$"^^La Te X ep
in defining formulation dp "$A,B,C$ given matrices"^^La Te X ep
in defining formulation dp "$X$, Unknown Matrix"^^La Te X ep
description ap "matrix equation, typically used in the field of control theory"@en
wikidata I D ap Q3730848 ep

Sylvester Equation Controllabilityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SylvesterEquationControllability

Except for the use of the reduced matrices (tilde-notation), there is a formal similarity with the Lyapunov equations for the calculations of Gramians.
belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Matrix A ni
contains quantity op Control System Matrix A (Reduced) ni
contains quantity op Control System Matrix B ni
contains quantity op Control System Matrix B (Reduced) ni
contains quantity op Unknown Matrix ni
generalizes formulation op Lyapunov Equation Controllability ni
defining formulation dp "$AX + X\tilde{A}^{*} + B\tilde{B}^{*} = 0$"^^La Te X ep
in defining formulation dp "$A$, Control System Matrix A"^^La Te X ep
in defining formulation dp "$B$, Control System Matrix B"^^La Te X ep
in defining formulation dp "$X$, Unknown Matrix"^^La Te X ep
in defining formulation dp "$\tilde{A}$, Control System Matrix A (Reduced)"^^La Te X ep
in defining formulation dp "$\tilde{B}$, Control System Matrix B (Reduced)"^^La Te X ep
description ap "Sylvester equation for the controllability of a linear control system"@en

Sylvester Equation Observabilityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SylvesterEquationObservability

Except for the use of the reduced matrices (tilde-notation), there is a formal similarity with the Lyapunov equations for the calculations of Gramians. However, note the sign change in the CC term.
belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Matrix A ni
contains quantity op Control System Matrix A (Reduced) ni
contains quantity op Control System Matrix C ni
contains quantity op Control System Matrix C (Reduced) ni
contains quantity op Unknown Matrix ni
generalizes formulation op Lyapunov Equation Observability ni
defining formulation dp "$\tilde{A}Y + YA^{*} - C\tilde{C}^{*} = 0$"^^La Te X ep
in defining formulation dp "$A$, Control System Matrix A"^^La Te X ep
in defining formulation dp "$C$, Control System Matrix C"^^La Te X ep
in defining formulation dp "$\tilde{A}$, Control System Matrix A (Reduced)"^^La Te X ep
in defining formulation dp "$\tilde{C}$, Control System Matrix C (Reduced)"^^La Te X ep
in defining formulation dp "$Υ$, Unknown Matrix"^^La Te X ep
description ap "Sylvester equation for the observability of a linear control system"@en

Sylvester Generalized Controllabilityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SylvesterGeneralizedControllability

Except for the use of the reduced matrices (tilde-notation), there is a formal similarity with the generalized Lyapunov equations for the calculations of generalized Gramians.
belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Matrix A (Reduced) ni
contains quantity op Control System Matrix B (Reduced) ni
contains quantity op Control System Matrix N (Reduced) ni
generalizes formulation op Lyapunov Generalized Controllability ni
generalizes formulation op Sylvester Equation Controllability ni
defining formulation dp "$AX + X\tilde{A}^{*} + \sum_kN_kX\tilde{N}_k^{*} + B\tilde{B}^{*} = 0$"^^La Te X ep
in defining formulation dp "$A$, Control System Matrix A (Reduced)"^^La Te X ep
in defining formulation dp "$B$, Control System Matrix B (Reduced)"^^La Te X ep
in defining formulation dp "$N$, Control System Matrix N (Reduced)"^^La Te X ep
description ap "generalized Sylvester equation for the controllability of a bi-linear control system"@en

Sylvester Generalized Observabilityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SylvesterGeneralizedObservability

Except for the use of the reduced matrices (tilde-notation), there is a formal similarity with the generalized Lyapunov equations for the calculations of generalized Gramians. However, note the sign change in the CC term.
belongs to
Mathematical Formulation c
has facts
contains quantity op Control System Matrix A (Reduced) ni
contains quantity op Control System Matrix C (Reduced) ni
contains quantity op Control System Matrix N (Reduced) ni
generalizes formulation op Sylvester Equation Observability ni
defining formulation dp "$\tilde{A}Y + YA^{*} + \sum_k\tilde{N}_kYN_k^{*} - C\tilde{C}^{*} = 0$"^^La Te X ep
in defining formulation dp "$A$, Control System Matrix A (Reduced)"^^La Te X ep
in defining formulation dp "$C$, Control System Matrix C (Reduced)"^^La Te X ep
in defining formulation dp "$N$, Control System Matrix N (Reduced)"^^La Te X ep
description ap "generalized Sylvester equation for the observability of a bi-linear control system"

Symmetric Top (Combined)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SymmetricTopCombined

Modeling a polar oblate (e.g. C6H6) or prolate (e.g. CH3Cl) molecule as a rigid symmetric top, interacting through both its permanent and induced electric dipole moment with electric fields. Note that analytical solutions to the TISE are available, see corresponding Task.
belongs to
Mathematical Model c
has facts
applied by task op Optimal Control ni
applied by task op Quantum Conditional Quasi-Solvability ni
applied by task op Quantum Stationary States ni
applied by task op Quantum Time Evolution ni
contains formulation op Molecular Alignment ni
contains formulation op Molecular Orientation ni
contains formulation op Quantum Hamiltonian (Electric Dipole) ni
contains formulation op Quantum Hamiltonian (Electric Polarizability) ni
contains formulation op Quantum Hamiltonian (Symmetric Top) ni
models op Molecular Rotation ni
description ap "modeling a polar oblate or prolate molecule as a rigid symmetric top, interacting with electric fields"@en

Symmetry Analysis In TEM Imagesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SymmetryAnalysisTEMImages

belongs to
Computational Task c
has facts
applies model op Dynamical Electron Scattering Model ni
description ap "symmetry analysis of TEM (transmission electron microscopy) images of crystals with strain"@en
doi I D ap rspa.2022.0317 ep

Symptomatic Infection Rateni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#SymptomaticInfectionRate

belongs to
Quantity c
has facts
generalized by quantity op Rate ni
description ap "constant representing the symptomatic infection rate"@en

Tangential Interaction Force Of Two Particlesni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Tangential_Interaction_Force_Of_Two_Particles

belongs to
Mathematical Formulation c
has facts
contained as formulation in op Linear Discrete Element Method ni
defining formulation dp "$\bm F^T_{ij}=-k^T_{ij}\bm\xi_{ij}-d^T_{ij}\dot{\bm \xi}_{ij}$"^^La Te X ep
in defining formulation dp "$\bm F_{ij}^T$, tangential interaction force"^^La Te X ep
in defining formulation dp "$\bm \xi'=\bm x_{C_{ji}}-\bm x_{C_{ij}}$"^^La Te X ep
in defining formulation dp "$\bm \xi^T_{ij}=\xi'{ij}-\langle \bm\xi_{ij}',\bm n_{ij}\rangle \bm n_{ij}$"^^La Te X ep
in defining formulation dp "$\bm t = \bm \xi_{ij} / \lVert \bm \xi_{ij}\rVert$, tangential unit vector"^^La Te X ep
in defining formulation dp "$\bm x_{C_{ij}}$, global contact point between particles $i$ and $j$"^^La Te X ep
in defining formulation dp "$\dot{\bm \xi}_{ij}=\langle \bm v_i-\bm v_j, \bm t\rangle \bm t$, tangential component of relative veloctiy"^^La Te X ep
description ap "tangential component of the total force, i.e. the sum of dissipative and conservative force"@en

Temperatureni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Temperature

Physical property of matter that quantitatively expresses the common notions of hot and cold
belongs to
Quantity Kind c
has facts
qudt I D ap Temperature ep
wikidata I D ap Q11466 ep

Tendon Lengthni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TendonLength

belongs to
Quantity c
has facts
generalized by quantity op Length ni
description ap "measurement of the distance from one end of a tendon to the other"@en

Tendon Strainni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TendonStrain

Definition of the tendon strain by length of tendon under stress and stress-free length of tendon
belongs to
Quantity c
has facts
defined by op Tendon Strain (Definition) ni
description ap "stretching or partially tearing a tendon"@en

Tendon Strain (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TendonStrainDefinition

belongs to
Mathematical Formulation c
has facts
contains quantity op Stress Free Tendon Length ni
contains quantity op Tendon Length ni
contains quantity op Tendon Strain ni
contains quantity op Time ni
defines op Tendon Strain ni
defining formulation dp "$\epsilon_{\text{T}(t) \equiv \frac{\mathcal{l}_\text{T}(t)-\mathcal{l}^{\text{slack}}_\text{T} }{\mathcal{l}^{\text{slack}}_\text{T}}$"^^La Te X ep
in defining formulation dp "$\epsilon_{\text{T}$, Tendon Strain"^^La Te X ep
in defining formulation dp "$\mathcal{l}^{\text{slack}}_\text{T}$, Stress Free Tendon Length"^^La Te X ep
in defining formulation dp "$l_{\text{T}}$, Tendon Length"^^La Te X ep
in defining formulation dp "$t$, Time"^^La Te X ep
description ap "stretching or partially tearing a tendon"@en

Thermal Conductivityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#HeatConductivity

belongs to
Quantity c
has facts
contained in formulation op Fourier Equation ni
description ap "capacity of a material to conduct heat"@en
qudt I D ap Thermal Conductivity ep
wikidata I D ap Q487005 ep

Timeni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Time

Dimension in which events can be ordered from the past through the present into the future
belongs to
Quantity Kind c
has facts
contained in formulation op Classical Hamilton Equations ni
contained in formulation op Classical Newton Equation ni
contained in formulation op Quantum Liouville Equation ni
contained in formulation op Schrödinger Equation (Time Dependent) ni
qudt I D ap Time ep
wikidata I D ap Q11471 ep

Time Pointni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TimePoint

ith time point
belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
description ap "instant of time"@en

Time Stepni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TimeStep

belongs to
Quantity c
has facts
generalized by quantity op Time ni
description ap "Incremental time step, typically used in temporal discretization of evolution equations"@en

Torqueni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Torque

tendency of a force to rotate an object
belongs to
Quantity Kind c
has facts
qudt I D ap Torque ep
wikidata I D ap Q48103 ep

Torque Of Particleni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Torque_Of_Particle

angular velocity needs to be taken into account when transforming the contact point between two particles from local to global coordinates
belongs to
Mathematical Formulation c
has facts
contained as formulation in op Linear Discrete Element Method ni
defining formulation dp "$\mathbf T_i = (\mathbf x_{a_{ij}} - \mathbf x_i)\times \mathbf F_T$"^^La Te X ep
in defining formulation dp "$\mathbf F_T$, tangential interaction force between particles $i$ and $j$"^^La Te X ep
in defining formulation dp "$\mathbf T_i$, torque acting on particle $i$"^^La Te X ep
in defining formulation dp "$\mathbf x_i$, position of particle $i$"^^La Te X ep
in defining formulation dp "$\mathbf x_{a_{ij}} = \mathbf x_i + \frac{r_i}{r_i + r_j}(\mathbf x_i - \mathbf x_j)$, actuation point, i.e. mid-point of contact area between particles $i$ and $j$ with radii $r_i$ and $r_j$"^^La Te X ep

Total Number Of Individualsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TotalNumberOfIndividuals

belongs to
Quantity c
has facts
description ap "overall count of people residing within a specific area"@en

Total Population Densityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TotalPopulationDensity

typically expressed as the number of people per square kilometer or square mile
belongs to
Quantity c
has facts
description ap "number of people living in a given area"@en

Total Population Density Formulationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TotalPopulationDensityFormulation

belongs to
Mathematical Formulation c
has facts
contained as formulation in op PDE SEIR Model ni
contains quantity op Density Fraction Coefficient ni
contains quantity op Isotropic Gaussian Function ni
contains quantity op Total Population Density ni
defining formulation dp "$n(x) \equiv \sum_{\tilde{l}=1}^{\tilde{L}} w_n^{(\tilde{l})} G^{(\tilde{l})}(x)$"^^La Te X ep
in defining formulation dp "$G^{(\tilde{l})}(x)$, Isotropic Gaussian Function"^^La Te X ep
in defining formulation dp "$n(x)$, Total Population Density"^^La Te X ep
in defining formulation dp "$w_n^{(\tilde{l})} $, Density Fraction Coefficient"^^La Te X ep
description ap "represented as a sum of Isotropic Gaussian functions of all provinces"@en

Total Population Sizeni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TotalPopulationSize

Total size of the population used in SI, SIR and SIS models. In the PDE SEIR model, superscript 'l' denotes the subdomain. superscript i denotes the ith subpopulation. if no i is provided, then it is a single-population model.
belongs to
Quantity c
has facts
generalized by quantity op Integer Number (Dimensionless) ni
is dimensionless dp "true"^^boolean
description ap "countable quantity representing the number of individuals"@en

Traffic Loadni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TrafficLoad

belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
description ap "number of passengers traveling along each edge in the public transportation network"@en

Transmembrane Potentialni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TransmembranePotential

Membrane potential (also transmembrane potential or membrane voltage) is the difference in electric potential between the interior and the exterior of a biological cell.
belongs to
Quantity c
is same as
Membrane Potential ni
has facts
generalized by quantity op Electric Potential ni
description ap "difference in electric potential between the interior and the exterior of a biological cell"@en
alt Label ap "Membrane Potential"@en
alt Label ap "Membrane Voltage"@en
wikidata I D ap Q389844 ep

Transmission Electron Microscopyni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TransmissionElectronMicroscopy

As such, TEM has become an indispensable experimental tool to examine objects in life sciences or in material sciences at nanoscales. See also WIAS annual report 2021
belongs to
Research Field c
has facts
description ap "uses the propagation of electron waves through magnetic lenses to create images of, e.g., the crystallographic structure of materials down to an atomic scale"@en
wikidata I D ap Q110779037 ep

Transport Equationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TransportEquation

There are several (constitutive) equations which describe the transport of matter, or properties of it, in an almost identical way. In every case, in words they read: Flux (density) is proportional to a gradient, where the constant of proportionality is a characteristic of the material. In general, the constant must be replaced by a 2nd rank tensor, to account for directional dependencies of the material.
belongs to
Mathematical Formulation c
has facts
generalizes formulation op Darcy Equation ni
generalizes formulation op Hooke Law (Linear Elasticity) ni
generalizes formulation op Ohm Equation ni
description ap "equation that describes the transport of some (extensive) quantity such as mass, energy|heat, momentum, electric charge"@en
wikidata I D ap Q105560509 ep

Transport Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TransportModel

There are several (constitutive) equations which describe the transport of matter, or properties of it, in an almost identical way. In every case, in words they read: Flux (density) is proportional to a gradient, where the constant of proportionality is a characteristic of the material. In general, the constant must be replaced by a 2nd rank tensor, to account for directional dependencies of the material.
belongs to
Mathematical Model c
has facts
contains formulation op Transport Equation ni
generalizes model op Charge Transport Model ni
generalizes model op Darcy Model ni
generalizes model op Diffusion Model ni
generalizes model op Heat Conduction Model ni
description ap "constitutive law describing the transport of matter, or properties of it, where the is proportional to a gradient"@en

Transport of Matterni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TransportOfMatter

belongs to
Research Problem c
has facts
contained in field op Continuum Mechanics ni
generalizes problem op Charge Transport ni
generalizes problem op Flow in porous media ni
generalizes problem op Heat Transport ni
generalizes problem op Species Transport ni
modeled by op Transport Model ni
description ap "transport of matter or of properties thereof"@en

Transport Routeni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TransportRoute

belongs to
Quantity Kind c
has facts
generalizes quantity op PTN Line ni
wikidata I D ap "https://www.wikidata.org/wiki/Q1297806"

Transportation Planningni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TransportationPlanning

belongs to
Research Field c
has facts
description ap "planning of transportation networks and traffic"@en
wikidata I D ap "https://www.wikidata.org/wiki/Q1034047"

Turn Over Timeni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#TurnOverTime

Time between two events, e.g. minimal time between services of lines in public transport
belongs to
Quantity c
has facts
generalized by quantity op Time ni
description ap "Time between two events"@en

Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UncompetitiveInhibitionConstantUniUniReactionReversibleInhibition

belongs to
Quantity c
has facts
generalized by quantity op Concentration ni
is dimensionless dp "false"^^boolean
description ap "constant for the uncompetitive inhibition in an uni uni reaction"@en

Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) Definitionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UncompetitiveInhibitionConstantUniUniReactionCompetitiveInhibitionDefinition

Definition of the Uncompetitive Inhibition Constant in an Uni Uni Reaction with a reversible Inhibition
belongs to
Mathematical Formulation c
has facts
contains quantity op Reaction Rate Constant ni
contains quantity op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
defines op Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition) ni
defining formulation dp "$K_{iu} \equiv \frac{k_{-4}}{k_4} $"^^La Te X ep
in defining formulation dp "$K_{iu}$, Uncompetitive Inhibition Constant (Uni Uni Reaction Reversible Inhibition)"^^La Te X ep
in defining formulation dp "$k_4$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-4}$, Reaction Rate Constant"^^La Te X ep
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean

Uni Uni Reactionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReaction

Enzyme (E) and Substrate (S) form an enzyme-substrate complex (ES), which catalyzes the formation of product (P). Depletion of product is also possible. Rates for complex formation and dissociation are $k_{1}$ and $k_{-1}$, $k_{2}$ and $k_{-2}$ are the rates of the rate-determining enzymatic step of product formation/depletion.
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni

Uni Uni Reaction (ODE Model)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionODEModel

Ordinary differential equations for the rates of change of all chemical species (substrate, enzyme, enzyme-substrate complex, product) in an Uni Uni reaction. $k_{i}$ with positive or negative i represents the rate constant of the forward- or backward-reaction i-th reaction step.
belongs to
Mathematical Model c
has facts
applied by task op Parameter Estimation of Enzyme Kinetics ni
applied by task op Sensitivity Analysis of Complex Kinetic Systems ni
applied by task op Simulation of Complex Kinetic Systems ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains formulation op Uni Uni Reaction ODE System ni
contains initial condition op Initial Enzyme Concentration (Uni Uni Reaction - ODE Model) ni
contains initial condition op Initial Enzyme - Substrate - Complex Concentration (Uni Uni Reaction - ODE Model) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction - ODE Model) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction - ODE Model) ni
generalizes model op Uni Uni Reaction (Michaelis Menten Model with Product - Steady State Assumption) ni
generalizes model op Uni Uni Reaction (Michaelis Menten Model without Product - Irreversibility Assumption) ni
generalizes model op Uni Uni Reaction (Michaelis Menten Model without Product - Rapid Equilibrium Assumption) ni
generalizes model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Uni Uni Reaction ni
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "true"^^boolean
is linear dp "false"^^boolean
is time-continuous dp "true"^^boolean
description ap "uni uni reaction model"@en

Uni Uni Reaction Competitive Complete Inhibition (Dixon Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionCompetitiveCompleteInhibitionDixonModelwithoutProductSteadyStateAssumption

belongs to
Mathematical Model c
has facts
applied by task op Linear Parameter Estimation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Dixon Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Dixon Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption) ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
linearizes model op Uni Uni Reaction Competitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Competitive Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean
description ap "uni uni reaction Dixon model without product and competitive complete Inhibition via the steady state assumption"@en

Uni Uni Reaction Competitive Complete Inhibition (Eadie Hofstee Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionCompetitiveCompleteInhibitionEadieHofsteeModelwithoutProductSteadyStateAssumption

belongs to
Mathematical Model c
has facts
applied by task op Linear Parameter Estimation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Eadie Hofstee Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Eadie Hofstee Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption) ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
linearizes model op Uni Uni Reaction Competitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Competitive Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean
description ap "uni uni reaction Eadie Hofstee model without product and competitive complete Inhibition via the steady state assumption"@en

Uni Uni Reaction Competitive Complete Inhibition (Hanes Woolf Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionCompetitiveCompleteInhibitionHanesWoolfModelwithoutProductSteadyStateAssumption

belongs to
Mathematical Model c
has facts
applied by task op Linear Parameter Estimation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Hanes Woolf Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Enzyme Conservation ni
contains formulation op Hanes Woolf Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption) ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
linearizes model op Uni Uni Reaction Competitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Competitive Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean
description ap "uni uni reaction Hanes Woolf model without Product and competitive complete Inhibition via the steady state assumption"@en

Uni Uni Reaction Competitive Complete Inhibition (Lineweaver Burk Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionCompetitiveCompleteInhibitionLineweaverBurkModelwithoutProductSteadyStateAssumption

belongs to
Mathematical Model c
has facts
applied by task op Linear Parameter Estimation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Lineweaver Burk Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Enzyme Conservation ni
contains formulation op Lineweaver Burk Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption) ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
linearizes model op Uni Uni Reaction Competitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Competitive Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean
description ap "uni uni reaction Lineweaver Burk model without product and competitive complete Inhibition via the steady state assumption"@en

Uni Uni Reaction Competitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionCompetitiveCompleteInhibitionMichaelisMentenModelwithoutProductSteadyStateAssumption

belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Michaelis Menten Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Competitive Complete Inhibition - Steady State Assumption) ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Competitive Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean
description ap "uni uni reaction Michaelis Menten model without product and competitive complete Inhibition via the steady state assumption"@en

Uni Uni Reaction Competitive Partial Inhibition (Michaelis Menten Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionCompetitivePartialInhibitionMichaelisMentenModelwithoutProductSteadyStateAssumption

belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Competitive Partial Inhibition - Michaelis Menten Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Competitive Partial Inhibition - Steady State Assumption) ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Competitive Partial Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean
description ap "uni uni reaction Michaelis Menten model without product and competitive partial Inhibition via the steady state assumption"@en

Uni Uni Reaction Mixed Complete Inhibition (Dixon Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionMixedCompleteInhibitionDixonModelwithoutProductSteadyStateAssumption

belongs to
Mathematical Model c
has facts
applied by task op Linear Parameter Estimation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Dixon Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains coupling condition op Mixed Enzyme Inhibition Coupling Condition (Uni Uni Reaction) ni
contains formulation op Dixon Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction Competitive Complete Inhibition (Dixon Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction Uncompetitive Complete Inhibition (Dixon Model without Product - Steady State Assumption) ni
linearizes model op Uni Uni Reaction Mixed Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Mixed Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean
description ap "uni uni reaction Dixon model without product and mixed complete Inhibition via the steady state assumption"@en

Uni Uni Reaction Mixed Complete Inhibition (Eadie Hofstee Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionMixedCompleteInhibitionEadieHofsteeModelwithoutProductSteadyStateAssumption

belongs to
Mathematical Model c
has facts
applied by task op Linear Parameter Estimation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Eadie Hofstee Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains coupling condition op Mixed Enzyme Inhibition Coupling Condition (Uni Uni Reaction) ni
contains formulation op Eadie Hofstee Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction Competitive Complete Inhibition (Eadie Hofstee Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction Uncompetitive Complete Inhibition (Eadie Hofstee Model without Product - Steady State Assumption) ni
linearizes model op Uni Uni Reaction Mixed Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Mixed Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean
description ap "uni uni reaction Eadie Hofstee model without product and mixed complete Inhibition via the steady state assumption"@en

Uni Uni Reaction Mixed Complete Inhibition (Hanes Woolf Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionMixedCompleteInhibitionHanesWoolfModelwithoutProductSteadyStateAssumption

belongs to
Mathematical Model c
has facts
applied by task op Linear Parameter Estimation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Hanes Woolf Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains coupling condition op Mixed Enzyme Inhibition Coupling Condition (Uni Uni Reaction) ni
contains formulation op Enzyme Conservation ni
contains formulation op Hanes Woolf Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction Competitive Complete Inhibition (Hanes Woolf Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction Uncompetitive Complete Inhibition (Hanes Woolf Model without Product - Steady State Assumption) ni
linearizes model op Uni Uni Reaction Mixed Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Mixed Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean
description ap "uni uni reaction Hanes Woolf model without product and mixed complete Inhibition via the steady state assumption"@en

Uni Uni Reaction Mixed Complete Inhibition (Lineweaver Burk Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionMixedCompleteInhibitionLineweaverBurkModelwithoutProductSteadyStateAssumption

belongs to
Mathematical Model c
has facts
applied by task op Linear Parameter Estimation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Lineweaver Burk Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains coupling condition op Mixed Enzyme Inhibition Coupling Condition (Uni Uni Reaction) ni
contains formulation op Enzyme Conservation ni
contains formulation op Lineweaver Burk Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction Competitive Complete Inhibition (Lineweaver Burk Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction Uncompetitive Complete Inhibition (Lineweaver Burk Model without Product - Steady State Assumption) ni
linearizes model op Uni Uni Reaction Mixed Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Mixed Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean
description ap "uni uni reaction Lineweaver Burk model without product and mixed complete Inhibition via the steady state assumption"@en

Uni Uni Reaction Mixed Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionMixedCompleteInhibitionMichaelisMentenModelwithoutProductSteadyStateAssumption

belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Michaelis Menten Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains coupling condition op Mixed Enzyme Inhibition Coupling Condition (Uni Uni Reaction) ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Mixed Complete Inhibition - Steady State Assumption) ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction Competitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction Uncompetitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Mixed Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean
description ap "uni uni reaction Michaelis Menten model without product and mixed complete Inhibition via the steady state assumption"@en

Uni Uni Reaction Mixed Partial Inhibition (Michaelis Menten Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionMixedPartialInhibitionMichaelisMentenModelwithoutProductSteadyStateAssumption

belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Mixed Partial Inhibition - Michaelis Menten Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains coupling condition op Mixed Enzyme Inhibition Coupling Condition (Uni Uni Reaction) ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Mixed Partial Inhibition - Steady State Assumption) ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction Competitive Partial Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction Uncompetitive Partial Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Mixed Partial Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean
description ap "uni uni reaction Michaelis Menten model without product and mixed partial Inhibition via the steady state assumption"@en

Uni Uni Reaction Non-Competitive Complete Inhibition (Dixon Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionNonCompetitiveCompleteInhibitionDixonModelwithoutProductSteadyStateAssumption

belongs to
Mathematical Model c
has facts
applied by task op Linear Parameter Estimation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Dixon Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains coupling condition op Non-Competitive Enzyme Inhibition Coupling Condition (Uni Uni Reaction) ni
contains formulation op Dixon Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption) ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction Competitive Complete Inhibition (Dixon Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction Uncompetitive Complete Inhibition (Dixon Model without Product - Steady State Assumption) ni
generalized by model op Uni Uni Reaction Mixed Complete Inhibition (Dixon Model without Product - Steady State Assumption) ni
linearizes model op Uni Uni Reaction Non-Competitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Non-Competitive Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean
description ap "uni uni reaction Dixon model without product and non-competitive complete Inhibition via the steady state assumption"@en

Uni Uni Reaction Non-Competitive Complete Inhibition (Eadie Hofstee Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionNonCompetitiveCompleteInhibitionEadieHofsteeModelwithoutProductSteadyStateAssumption

belongs to
Mathematical Model c
has facts
applied by task op Linear Parameter Estimation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Eadie Hofstee Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains coupling condition op Non-Competitive Enzyme Inhibition Coupling Condition (Uni Uni Reaction) ni
contains formulation op Eadie Hofstee Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption) ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction Competitive Complete Inhibition (Eadie Hofstee Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction Uncompetitive Complete Inhibition (Eadie Hofstee Model without Product - Steady State Assumption) ni
generalized by model op Uni Uni Reaction Mixed Complete Inhibition (Eadie Hofstee Model without Product - Steady State Assumption) ni
linearizes model op Uni Uni Reaction Non-Competitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Non-Competitive Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean
description ap "uni uni reaction Eadie-Hofstee model without product and non-competitive complete Inhibition via the steady state assumption"@en

Uni Uni Reaction Non-Competitive Complete Inhibition (Hanes Woolf Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionNonCompetitiveCompleteInhibitionHanesWoolfModelwithoutProductSteadyStateAssumption

belongs to
Mathematical Model c
has facts
applied by task op Linear Parameter Estimation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Hanes Woolf Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains coupling condition op Non-Competitive Enzyme Inhibition Coupling Condition (Uni Uni Reaction) ni
contains formulation op Enzyme Conservation ni
contains formulation op Hanes Woolf Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption) ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction Competitive Complete Inhibition (Hanes Woolf Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction Uncompetitive Complete Inhibition (Hanes Woolf Model without Product - Steady State Assumption) ni
generalized by model op Uni Uni Reaction Mixed Complete Inhibition (Hanes Woolf Model without Product - Steady State Assumption) ni
linearizes model op Uni Uni Reaction Non-Competitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Non-Competitive Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean
description ap "uni uni reaction Hanes Woolf model without product and non-competitive complete Inhibition via the steady state assumption"@en

Uni Uni Reaction Non-Competitive Complete Inhibition (Lineweaver Burk Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionNonCompetitiveCompleteInhibitionLineweaverBurkModelwithoutProductSteadyStateAssumption

belongs to
Mathematical Model c
has facts
applied by task op Linear Parameter Estimation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Lineweaver Burk Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains coupling condition op Non-Competitive Enzyme Inhibition Coupling Condition (Uni Uni Reaction) ni
contains formulation op Enzyme Conservation ni
contains formulation op Lineweaver Burk Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption) ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction Competitive Complete Inhibition (Lineweaver Burk Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction Uncompetitive Complete Inhibition (Lineweaver Burk Model without Product - Steady State Assumption) ni
generalized by model op Uni Uni Reaction Mixed Complete Inhibition (Lineweaver Burk Model without Product - Steady State Assumption) ni
linearizes model op Uni Uni Reaction Non-Competitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Non-Competitive Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean
description ap "uni uni reaction Lineweaver Burk model without product and non-competitive complete Inhibition via the steady state assumption"@en

Uni Uni Reaction Non-Competitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionNonCompetitiveCompleteInhibitionMichaelisMentenModelwithoutProductSteadyStateAssumption

belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Michaelis Menten Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains coupling condition op Non-Competitive Enzyme Inhibition Coupling Condition (Uni Uni Reaction) ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Non-Competitive Complete Inhibition - Steady State Assumption) ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction Competitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction Uncompetitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
generalized by model op Uni Uni Reaction Mixed Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Non-Competitive Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean
description ap "uni uni reaction Michaelis Menten model without product and non-competitive complete Inhibition via the steady state assumption"@en

Uni Uni Reaction Non-Competitive Partial Inhibition (Michaelis Menten Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionNonCompetitivePartialInhibitionMichaelisMentenModelwithoutProductSteadyStateAssumption

belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Non-Competitive Partial Inhibition - Michaelis Menten Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains coupling condition op Non-Competitive Enzyme Inhibition Coupling Condition (Uni Uni Reaction) ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Non-Competitive Partial Inhibition - Steady State Assumption) ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction Competitive Partial Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
contains model op Uni Uni Reaction Uncompetitive Partial Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
generalized by model op Uni Uni Reaction Mixed Partial Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Non-Competitive Partial Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean
description ap "uni uni reaction Dixon model without product and non-competitive partial Inhibition via the steady state assumption"@en

Uni Uni Reaction ODE Systemni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionODESystem

ODE System describing an Uni Uni Reaction over time
belongs to
Mathematical Formulation c
has facts
contains formulation op Enzyme Concentration ODE (Uni Uni Reaction) ni
contains formulation op Enzyme - Substrate - Complex Concentration ODE (Uni Uni Reaction) ni
contains formulation op Product Concentration ODE (Uni Uni Reaction) ni
contains formulation op Substrate Concentration ODE (Uni Uni Reaction) ni
contains quantity op Concentration ni
contains quantity op Reaction Rate Constant ni
contains quantity op Reaction Rate ni
contains quantity op Time ni
defining formulation dp "$\begin{align} \frac{dc_{S}}{dt}&=-k_{1}*c_{E}*c_{S}+k_{-1}*c_{ES} \\ \frac{dc_{P}}{dt}&=k_{2}*c_{ES}-k_{-2}*c_{E}*c_{P} \\ \frac{dc_{E}}{dt}&=-k_{1}*c_{E}*c_{S}+k_{-1}*c_{ES}+k_{2}*c_{ES}-k_{-2}*c_{E}*c_{P} \\ \frac{dc_{ES}}{dt}&=k_{1}*c_{E}*c_{S}-k_{-1}*c_{ES}-k_{2}*c_{ES}+k_{-2}*c_{E}*c_{P} \end{align}$"^^La Te X ep
in defining formulation dp "$\frac{dc_{ES}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$\frac{dc_{E}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$\frac{dc_{P}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$\frac{dc_{S}}{dt}$, Reaction Rate"^^La Te X ep
in defining formulation dp "$c_{ES}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{E}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{P}$, Concentration"^^La Te X ep
in defining formulation dp "$c_{S}$, Concentration"^^La Te X ep
in defining formulation dp "$k_{-1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{-2}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{1}$, Reaction Rate Constant"^^La Te X ep
in defining formulation dp "$k_{2}$, Reaction Rate Constant"^^La Te X ep

Uni Uni Reaction Uncompetitive Complete Inhibition (Dixon Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionUncompetitiveCompleteInhibitionDixonModelwithoutProductSteadyStateAssumption

belongs to
Mathematical Model c
has facts
applied by task op Linear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Dixon Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Dixon Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption) ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
linearizes model op Uni Uni Reaction Uncompetitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Uncompetitive Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean
description ap "uni uni reaction Dixon model without product and uncompetitive complete Inhibition via the steady state assumption"@en

Uni Uni Reaction Uncompetitive Complete Inhibition (Eadie Hofstee Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionUncompetitiveCompleteInhibitionEadieHofsteeModelwithoutProductSteadyStateAssumption

belongs to
Mathematical Model c
has facts
applied by task op Linear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Eadie Hofstee Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Eadie Hofstee Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption) ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
linearizes model op Uni Uni Reaction Uncompetitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Uncompetitive Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean
description ap "uni uni reaction Eadie Hofstee model without product and uncompetitive complete Inhibition via the steady state assumption"@en

Uni Uni Reaction Uncompetitive Complete Inhibition (Hanes Woolf Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionUncompetitiveCompleteInhibitionHanesWoolfModelwithoutProductSteadyStateAssumption

belongs to
Mathematical Model c
has facts
applied by task op Linear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Hanes Woolf Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Enzyme Conservation ni
contains formulation op Hanes Woolf Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption) ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
linearizes model op Uni Uni Reaction Uncompetitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Uncompetitive Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean
description ap "uni uni reaction Hanes Woolf model without product and uncompetitive complete Inhibition via the steady state assumption"@en

Uni Uni Reaction Uncompetitive Complete Inhibition (Lineweaver Burk Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionUncompetitiveCompleteInhibitionLineweaverBurkModelwithoutProductSteadyStateAssumption

belongs to
Mathematical Model c
has facts
applied by task op Linear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Lineweaver Burk Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Enzyme Conservation ni
contains formulation op Lineweaver Burk Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption) ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
linearizes model op Uni Uni Reaction Uncompetitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Uncompetitive Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "true"^^boolean
description ap "uni uni reaction Lineweaver Burk model without product and uncompetitive complete Inhibition via the steady state assumption"@en

Uni Uni Reaction Uncompetitive Complete Inhibition (Michaelis Menten Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionUncompetitiveCompleteInhibitionMichaelisMentenModelwithoutProductSteadyStateAssumption

belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Michaelis Menten Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Uncompetitive Complete Inhibition - Steady State Assumption) ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Uncompetitive Complete Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean
description ap "uni uni reaction Michaelis Menten model without product and uncompetitive complete Inhibition via the steady state assumption"@en

Uni Uni Reaction Uncompetitive Partial Inhibition (Michaelis Menten Model without Product - Steady State Assumption)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionUncompetitivePartialInhibitionMichaelisMentenModelwithoutProductSteadyStateAssumption

belongs to
Mathematical Model c
has facts
applied by task op Nonlinear Parameter Estimation (Uni Uni Reaction without Product and Uncompetitive Partial Inhibition - Michaelis Menten Model - Steady State Assumption) ni
contains assumption op Excess Substrate Assumption ni
contains assumption op Steady State Assumption ni
contains formulation op Enzyme Conservation ni
contains formulation op Mass Action Law ni
contains formulation op Mass Balance Law ni
contains formulation op Michaelis Menten Equation (Uni Uni Reaction without Product and Uncompetitive Partial Inhibition - Steady State Assumption) ni
contains initial condition op Initial Inhibitor Concentration (Uni Uni Reaction) ni
contains initial condition op Initial Product Concentration (Uni Uni Reaction without Product) ni
contains initial condition op Initial Substrate Concentration (Uni Uni Reaction) ni
contains model op Uni Uni Reaction (Michaelis Menten Model without Product - Steady State Assumption) ni
models op Initial Reaction Rate of Uni Uni Reaction without Product and Uncompetitive Partial Inhibition ni
is convex dp "false"^^boolean
is deterministic dp "true"^^boolean
is dimensionless dp "false"^^boolean
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean
description ap "uni uni reaction Michaelis Menten model without product and uncompetitive partial Inhibition via the steady state assumption"@en

Uni Uni Reaction with Competitive Complete Inhibitionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionwithCompetitiveCompleteInhibition

Enzyme (E) and Substrate (S) form an enzyme-substrate complex (ES), which catalyzes the formation of product (P). Rates for complex formation and dissociation are $k_{1}$ and $k_{-1}$, $k_{2}$ is the rate of the rate-determining enzymatic step of product formation. Free enzyme may bind an inhibitor (I) to form an enzyme-inhibitor complex (EI) with rates $k_{3}$ and $k_{-3}$.
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni
generalized by problem op Uni Uni Reaction with Reversible Complete Inhibition ni
generalizes problem op Initial Reaction Rate of Uni Uni Reaction without Product and Competitive Complete Inhibition ni

Uni Uni Reaction with Competitive Partial Inhibitionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionwithCompetitivePartialInhibition

Enzyme (E) and Substrate (S) form an enzyme-substrate complex (ES), which catalyzes the formation of product (P). Rates for complex formation and dissociation are $k_{1}$ and $k_{-1}$, $k_{2}$ is the rate of the rate-determining enzymatic step of product formation. Free enzyme and the enzyme-substrate complex may bind an inhibitor (I) to form an enzyme-inhibitor (EI) and enzyme-inhibitor-substrate complex (EIS) with $k_{3}$ or $k_{-3}$ and $k_{4}$ or $k_{-4} as rates of inhibitor complex formation and depletion. Enzyme-inhibitor complex and enzyme-inhibitor-substrate convert into each other with rates $k_{5}$ and $k_{-5}$. From the enzyme-inhibitor-substrate complex product is formed with rate $k_{2}$. Properly this is a mixed partial inhibition in which the inhibitor does not affect the turnover rate,
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni
generalized by problem op Uni Uni Reaction with Reversible Partial Inhibition ni
generalizes problem op Initial Reaction Rate of Uni Uni Reaction without Product and Competitive Partial Inhibition ni

Uni Uni Reaction with Mixed Complete Inhibitionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionwithMixedCompleteInhibition

Enzyme (E) and Substrate (S) form an enzyme-substrate complex (ES), which catalyzes the formation of product (P). Rates for complex formation and dissociation are $k_{1}$ and $k_{-1}$, $k_{2}$ is the rate of the rate-determining enzymatic step of product formation. Free enzyme and the enzyme-substrate complex may bind an inhibitor (I) to form an enzyme-inhibitor (EI) and enzyme-inhibitor-substrate complex (EIS) with $k_{3}$ or $k_{-3}$ and $k_{4}$ or $k_{-4} as rates of inhibitor complex formation and depletion. Enzyme-inhibitor complex and enzyme-inhibitor-substrate convert into each other with rates $k_{5}$ and $k_{-5}$. From the enzyme-inhibitor-substrate complex no product formation is possible, the inhibition is thus complete.
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni
generalized by problem op Uni Uni Reaction with Reversible Complete Inhibition ni
generalizes problem op Initial Reaction Rate of Uni Uni Reaction without Product and Mixed Complete Inhibition ni

Uni Uni Reaction with Mixed Partial Inhibitionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionwithMixedPartialInhibition

Enzyme (E) and Substrate (S) form an enzyme-substrate complex (ES), which catalyzes the formation of product (P). Rates for complex formation and dissociation are $k_{1}$ and $k_{-1}$, $k_{2}$ is the rate of the rate-determining enzymatic step of product formation. Free enzyme and the enzyme-substrate complex may bind an inhibitor (I) to form an enzyme-inhibitor (EI) and enzyme-inhibitor-substrate complex (EIS) with $k_{3}$ or $k_{-3}$ and $k_{4}$ or $k_{-4} as rates of inhibitor complex formation and depletion. Enzyme-inhibitor complex and enzyme-inhibitor-substrate convert into each other with rates $k_{5}$ and $k_{-5}$. From the enzyme-inhibitor-substrate complex product is formed with rate $k_{6}$.
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni
generalized by problem op Uni Uni Reaction with Reversible Partial Inhibition ni
generalizes problem op Initial Reaction Rate of Uni Uni Reaction without Product and Mixed Partial Inhibition ni

Uni Uni Reaction with Non-Competitive Complete Inhibitionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionwithNonCompetitiveCompleteInhibition

Enzyme (E) and Substrate (S) form an enzyme-substrate complex (ES), which catalyzes the formation of product (P). Rates for complex formation and dissociation are $k_{1}$ and $k_{-1}$, $k_{2}$ is the rate of the rate-determining enzymatic step of product formation. Free enzyme and the enzyme-substrate complex may bind an inhibitor (I) to form an enzyme-inhibitor (EI) and enzyme-inhibitor-substrate complex (EIS) with $k_{3}$ or $k_{-3}$ and $k_{4}$ or $k_{-4} as rates of inhibitor complex formation and depletion. Enzyme-inhibitor complex and enzyme-inhibitor-substrate convert into each other with rates $k_{5}$ and $k_{-5}$. In the non-competitive case: $k_{3} = k_{4}$, $k_{-3} = k_{-4}$, $k_{5} = k_{1}$ and $k_{-5} = k_{-1}$. The enzyme-inhibitor-substrate complex cannot form product, the inhibition is thus complete.
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni
generalized by problem op Uni Uni Reaction with Reversible Complete Inhibition ni
generalizes problem op Initial Reaction Rate of Uni Uni Reaction without Product and Non-Competitive Complete Inhibition ni

Uni Uni Reaction with Non-Competitive Partial Inhibitionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionwithNonCompetitivePartialInhibition

Enzyme (E) and Substrate (S) form an enzyme-substrate complex (ES), which catalyzes the formation of product (P). Rates for complex formation and dissociation are $k_{1}$ and $k_{-1}$, $k_{2}$ is the rate of the rate-determining enzymatic step of product formation. Free enzyme and the enzyme-substrate complex may bind an inhibitor (I) to form an enzyme-inhibitor (EI) and enzyme-inhibitor-substrate complex (EIS) with $k_{3}$ or $k_{-3}$ and $k_{4}$ or $k_{-4} as rates of inhibitor complex formation and depletion. Enzyme-inhibitor complex and enzyme-inhibitor-substrate convert into each other with rates $k_{5}$ and $k_{-5}$. In the non-competitive case: $k_{3} = k_{4}$, $k_{-3} = k_{-4}$, $k_{5} = k_{1}$ and $k_{-5} = k_{-1}$. The enzyme-inhibitor-substrate complex can form product with rate $k_{6}.
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni
generalized by problem op Uni Uni Reaction with Reversible Partial Inhibition ni
generalizes problem op Initial Reaction Rate of Uni Uni Reaction without Product and Non-Competitive Partial Inhibition ni

Uni Uni Reaction with Reversible Complete Inhibitionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionwithReversibleCompleteInhibition

Uni Uni Reaction with reversible inhibition. The enzyme-inhibitor-substrate complex (EIS) cannot form product, the inhibition is thus complete.
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni

Uni Uni Reaction with Reversible Partial Inhibitionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionwithReversiblePartialInhibition

Uni Uni Reaction with reversible inhibition. The enzyme-inhibitor-substrate complex (EIS) can form product, the inhibition is thus partial.
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni

Uni Uni Reaction with Uncompetitive Complete Inhibitionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionwithUncompetitiveCompleteInhibition

Enzyme (E) and Substrate (S) form an enzyme-substrate complex (ES), which catalyzes the formation of product (P). Rates for complex formation and dissociation are $k_{1}$ and $k_{-1}$, $k_{2}$ is the rate of the rate-determining enzymatic step of product formation. Enzyme-substrate complex may bind an inhibitor (I) to form an enzyme-inhibitor-substrate complex (EIS) with rates $k_{4}$ and $k_{-4}$. The enzyme-inhibitor-substrate complex cannot form product, the inhibition is thus complete.
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni
generalized by problem op Uni Uni Reaction with Reversible Complete Inhibition ni
generalizes problem op Initial Reaction Rate of Uni Uni Reaction without Product and Uncompetitive Complete Inhibition ni

Uni Uni Reaction with Uncompetitive Partial Inhibitionni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniUniReactionwithUncompetitivePartialInhibition

Enzyme (E) and Substrate (S) form an enzyme-substrate complex (ES), which catalyzes the formation of product (P). Rates for complex formation and dissociation are $k_{1}$ and $k_{-1}$, $k_{2}$ is the rate of the rate-determining enzymatic step of product formation. Enzyme-substrate complex may bind an inhibitor (I) to form an enzyme-inhibitor-substrate complex (EIS) with rates $k_{4}$ and $k_{-4}$. The enzyme-inhibitor-substrate complex can form product with rate $k_{6}$.
belongs to
Research Problem c
has facts
contained in field op Enzyme Kinetics ni
generalized by problem op Uni Uni Reaction with Reversible Partial Inhibition ni
generalizes problem op Initial Reaction Rate of Uni Uni Reaction without Product and Uncompetitive Partial Inhibition ni

Uniform Gravitational Accelerationni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UniformGravitationalAcceleration

This is a very good approximation for an apple falling from a tree, but not for celestial mechanics where the inverse-square law of the gravitational field must be taken into account.
belongs to
Mathematical Formulation c
has facts
contains quantity op Earth Radius ni
contains quantity op Free Fall Height ni
defining formulation dp "$h \approx r$"^^La Te X ep
in defining formulation dp "$h$, Free Fall Height"^^La Te X ep
in defining formulation dp "$r$, Earth Radius"^^La Te X ep
description ap "assuming that the gravitational constant remains unchanged from the beginning to the end of a trajectory, e.g. a free fall"@en

Unit Normal Vectorni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UnitNormalVector

A vector that is normal to some surface (typically an interface), with unit length
belongs to
Quantity c
has facts
description ap "vector that is normal to some surface (typically an interface), with unit length"@en
wikidata I D ap Q91093255 ep

Unit Tangent Vectorni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UnitTangentVector

A vector that is tangent to a curve or surface at a given point, with unit length
belongs to
Quantity c
has facts
description ap "vector that is tangential to a curve or surface at a given point, with unit length"@en
wikidata I D ap Q106041131 ep

Unknown Matrixni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UnknownMatrix

belongs to
Quantity c
has facts
description ap "unknown matrix, to be found"@en

Upper-Triangular Matrixni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#UpperTriangularMatrix

belongs to
Quantity c
has facts
is dimensionless dp "true"^^boolean
description ap "matrix with all elements below the main diagonal equal to zero"@en

van Roosbroeck Modelni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#vanRoosbroeckModel

The van Roosbroeck system describes the semi-classical transport of free electrons and holes in a self-consistent electric field using a drift-diffusion approximation. It became the standard model to describe the current flow in semiconductor devices such as diodes, transistors, LEDs, solar cells and lasers, as well as quantum nanostructures and organic semiconductors.
belongs to
Mathematical Model c
is same as
Drift-Diffusion Model ni
has facts
contains formulation op Boltzmann Approximation For Electrons ni
contains formulation op Boltzmann Approximation For Holes ni
contains formulation op Continuity Equation For Electrons ni
contains formulation op Continuity Equation For Holes ni
contains formulation op Poisson Equation For The Electric Potential ni
surveyed in op Koprucki (2017) Numerical methods for drift-diffusion models ni
is dynamic dp "false"^^boolean
is linear dp "false"^^boolean
is space-continuous dp "true"^^boolean
description ap "mathematical model describing the semi-classical transport of free electrons and holes in a self-consistent electric field using a drift-diffusion approximation"@en
doi I D ap W I A S. P R E P R I N T.2263 ep
doi I D ap 9781315152318 25 ep

Vanishing Air Densityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#VanishingAirDensity

belongs to
Mathematical Formulation c
has facts
contains quantity op Density Of Air ni
defining formulation dp "$\rho\rightarrow 0$"^^La Te X ep
in defining formulation dp "$\rho$, Density of Air"^^La Te X ep
description ap "in the limit of vanishing air density, physical bodies will move like in vacuum, e.g. free fall models"@en

Vanishing Drag Coefficientni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#VanishingDragCoefficient

belongs to
Mathematical Formulation c
has facts
contains quantity op Drag Coefficient ni
defining formulation dp "$C_D\rightarrow 0$"^^La Te X ep
in defining formulation dp "$C_D$, Drag Coefficient"^^La Te X ep
description ap "in the limit of vanishing drag coefficient, physical bodies will move like in vacuum, e.g. free fall models"@en

Varianceni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Variance

belongs to
Quantity Kind c
has facts
wikidata I D ap Q175199 ep

Velocityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Velocity

Rate of change of the position of an object as a function of time, and the direction of that change
belongs to
Quantity Kind c
has facts
qudt I D ap Velocity ep
wikidata I D ap Q11465 ep

Vibration Frequency (Anharmonic)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#VibrationFrequencyAnharmonic

belongs to
Quantity c
has facts
generalizes quantity op Vibration Frequency (Harmonic) ni
description ap "frequency of oscillation in systems that deviate from the ideal harmonic oscillator model"@en
wikidata I D ap Q545228 ep

Vibration Frequency (Harmonic)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#VibrationFrequencyHarmonic

belongs to
Quantity c
has facts
generalized by quantity op Frequency ni
description ap "harmonic frequency of vibration, e.g. of a molecule"@en
wikidata I D ap Q677864 ep

Vibrational Frequency Shift (1st Order)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#VibrationalFrequencyShift1stOrder

The interpretation is quite straight-forward: Effectively, the intermolecular potential changes the effective force constant of a vibrational normal mode.
belongs to
Mathematical Formulation c
has facts
contains quantity op Intermolecular Potential ni
contains quantity op Normal Mode Coordinate (Dimensionless) ni
contains quantity op Quantum Eigen Energy ni
defining formulation dp "$E_{1,r}^{(1)}-E_{0,r}^{(1)}= \frac{1}{2} \frac{\partial^2U}{\partial q_r^2}$"^^La Te X ep
in defining formulation dp "$E$, Quantum Eigen Energy"^^La Te X ep
in defining formulation dp "$U$, Intermolecular Potential"^^La Te X ep
in defining formulation dp "$q$, Normal Mode Coordinate (Dimensionless)"^^La Te X ep
description ap "frequency shift of molecular vibrations caused by interaction with surrounding particles from 1st order non-degenerate perturbation theory"@en

Vibrational Frequency Shift (2nd Order)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#VibrationalFrequencyShift2ndOrder

The interpretation is based on the coupling of different vibrational normal modes, mediated by the cubic anharmonicity of the intramolecular force field.
belongs to
Mathematical Formulation c
has facts
contains quantity op Force Constant (Anharmonic) ni
contains quantity op Intermolecular Potential ni
contains quantity op Normal Mode Coordinate (Dimensionless) ni
contains quantity op Quantum Eigen Energy ni
contains quantity op Vibration Frequency (Harmonic) ni
defining formulation dp "$E_{1,r}^{(2)}-E_{0,r}^{(2)}= \frac{1}{2} \frac{\phi_{rrs}}{\omega_s} \frac{\partial U}{\partial q_s}$"^^La Te X ep
in defining formulation dp "$E$, Quantum Eigen Energy"^^La Te X ep
in defining formulation dp "$U$, Intermolecular Potential"^^La Te X ep
in defining formulation dp "$\omega$, Vibration Frequency Harmonic"^^La Te X ep
in defining formulation dp "$\phi$, Force Constant (Anharmonic)"^^La Te X ep
in defining formulation dp "$q$, Normal Mode Coordinate (Dimensionless)"^^La Te X ep
description ap "frequency shift of molecular vibrations caused by interaction with surrounding particles from 2nd order non-degenerate perturbation theory"@en

Viscosityni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Viscosity

Resistance of a fluid to shear deformation
belongs to
Quantity Kind c
has facts
qudt I D ap Viscosity ep
wikidata I D ap Q128709 ep

Viscous Dissipation Potentialni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ViscousDissipationPotential

belongs to
Quantity c
has facts
description ap "describes the conversion of mechanical energy into internal energy due to the viscosity of a fluid"@en

Voltageni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#ElectricVoltage

Difference in electric potential between two points (indicated in volt)
belongs to
Quantity Kind c
has facts
qudt I D ap Voltage ep
wikidata I D ap Q25428 ep

Wave Vector of an Electronni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#WaveVectorElectron

Vector pointing in the direction of a wave and whose magnitude is equal to the wavenumber. In quantum mechanics/condensed matter physics, a wave vector is the quotient of the momentum vektor of particles or quasi particles and the reduced Planck constant
belongs to
Quantity c
has facts
contained in formulation op Darwin-Howie-Whelan Equation for an unstrained crystal ni
contained in formulation op Darwin-Howie-Whelan Equation for a strained crystal ni
description ap "vector pointing in the direction of propagation of a wave and whose magnitude is equal to the wavenumber"@en
wikidata I D ap Q657009 ep

Weber (2022) The Mathematics of Comparing Objectsni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#Weber_2022_The_Mathematics_of_Comparing_Objects

belongs to
Publication c
has facts
invents op Object Comparison Model ni
arxiv I D ap 2201.07032v2 ep
doi I D ap ar Xiv.2201.07032 ep

Weight Factorni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#WeightFactor

belongs to
Quantity c
has facts
defined by op Weight Factor (Definition) ni
is dimensionless dp "true"^^boolean
description ap "maximum between the data and the standard deviation for region m observed in time"@en

Weight Factor (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#WeightFactorDefinition

belongs to
Mathematical Formulation c
has facts
contains quantity op Romanized Cities Vector ni
contains quantity op Weight Factor ni
defines op Weight Factor ni
defining formulation dp "$C_{m,t_i} \equiv \max \{ \omega _{m,t_i}, STD(\omega _{m,\bullet })\}$"^^La Te X ep
in defining formulation dp "$C$, Weight Factor"
in defining formulation dp "$\omega$, Romanized Cities Vector"
is deterministic dp "true"^^boolean
is dimensionless dp "true"^^boolean
is dynamic dp "true"^^boolean
description ap "definition of weighting factor"@en

White Noiseni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#WhiteNoise

Delta-correlated stationary Gaussian process with zero-mean, i.e., a random signal with equal intensity at all frequencies, yielding a constant power spectral density.
belongs to
Quantity c
has facts
description ap "delta-correlated stationary Gaussian process with zero-mean"@en
wikidata I D ap Q381287 ep

Wiener Processni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#WienerProcess

A stochastic process generalizing Brownian motion, used to represent the integral of a white noise Gaussian process,
belongs to
Quantity c
has facts
similar to quantity op White Noise ni
description ap "stochastic process generalizing Brownian motion"@en
wikidata I D ap Q1056809 ep

Young Modulusni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#YoungsModulus

belongs to
Quantity c
has facts
description ap "mechanical property that measures stiffness of a solid material"@en
alt Label ap "Elastic modulus"@en
alt Label ap "Modulus of elasticity"@en
alt Label ap "Young's modulus"@en
wikidata I D ap Q2091584 ep

Young Modulus (Definition)ni back to ToC or Named Individual ToC

IRI: https://mardi4nfdi.de/mathmoddb#YoungModulusDefinition

belongs to
Mathematical Formulation c
has facts
contains quantity op Linear Strain ni
contains quantity op Normal Stress ni
contains quantity op Young Modulus ni
defines op Young Modulus ni
defining formulation dp "$E \equiv \frac{\sigma}{\varepsilon}$"^^La Te X ep
in defining formulation dp "$E$, Young Modulus"^^La Te X ep
in defining formulation dp "$\sigma$, Normal Stress"^^La Te X ep
in defining formulation dp "$\varepsilon$, Linear Strain"^^La Te X ep
description ap "mechanical property that measures stiffness of a solid material"@en
wikidata I D ap Q2091584 ep

Legend back to ToC

c: Classes
op: Object Properties
dp: Data Properties
ni: Named Individuals
ep: External Properties

References back to ToC

Add your references here. It is recommended to have them as a list.

Acknowledgments back to ToC

The authors would like to thank Silvio Peroni for developing LODE, a Live OWL Documentation Environment, which is used for representing the Cross Referencing Section of this document and Daniel Garijo for developing Widoco, the program used to create the template used in this documentation.